What are the current problems facing the Palestinian Arabs under Israeli control?

Answer 1

Answer
First, we should separate the Palestinians who are citizens of Israel (and live within Israel proper) from the Palestinians who are citizens of the State of Palestine and live under Israeli military occupation in the West Bank. These two groups suffer differently to the degree that they do suffer.

It should be made clear that the Palestinians who suffer in the Gaza Strip are NOT under Israeli control since Israel maintains no army, navy, air force, police or other gubernatorial presence in Gaza at all; the area is completely enthralled to Hamas. Hamas is the only party responsible for vast human rights atrocities in the Gaza Strip like: the execution of protesters, the banning of female dancing and scooters, and the both the inane laws and use of torture by a vice and virtue police modeled after Saudi Arabia. (Also not discussed in this answer is Arab repression of Palestinians, which is often crueler than Israeli repression, see the Comment at the end of this Answer.)

Palestinian Citizens of Israel
It should be noted that the Palestinian Citizens of Israel have every right and privilege as the Jewish Citizens of Israel and every requirement in common save that Palestinian Citizens of Israel do not face mandatory conscription. Arabs, even Anti-Zionist Arabs, have been elected to all of the major offices of government. The suffering incurred by Palestinian Citizens in Israel comes from disproportionate effects of laws applied equally to Palestinian Citizens of Israel as Jewish Citizens of Israel on the Palestinian population. For example, for the easier maintenance of water and service provisioning, there are a number of laws that limit the expansion of municipal boundaries. This disproportionately affects Palestinian Citizens of Israel because they have a higher Birth Rate and their communities are expanding. This issue arises alongside the creation of new towns and villages or expanding current ones; not the loss of current territory. Additionally, when Jewish neighborhoods expand beyond legal boundaries, they are just as penalized. The only other grievance that Palestinian Citizens of Israel have is that they feel that the identity of the State of Israel does not represent them. What they fail to realize is that every nationalist state will have a dominant ethnicity and identity. Circassians, Druze, and Bedouins accept this, but Palestinians want to play this “feelings game”.

Palestinians Under Military Occupation in the Palestinian Territories
Being under a military occupation, there are a number of difficulties that Palestinians in the West Bank suffer through at Israeli hands:

1) Checkpoints and Barriers: The Israeli military has placed numerous checkpoints throughout the West Bank in order to minimize the possibility of terrorist attacks. Additionally, as another aspect of security, Israel has built a fence (and in some places a concrete wall) to stop Palestinian suicide bombings. However, the Security Fence cuts across Palestinian personal property, encircles Israeli Settlements, and cuts Palestinians off from a number of aquifers (which are necessary to provide water for a mostly agrarian Palestinian people).

2) Settlements and Land Confiscation: Land in the West Bank is confiscated according to a variety of arcane, inane, and relatively unjust laws (depending on your perspective) in order to create Israeli Jewish townships in the less-populous parts of the West Bank. In addition to the lands taken in order for the Settlers to live, Settlers have also taken sufficient lands to build highways and other infrastructure to connect the Settlements to 1949 Israel, bypassing Palestinian cities and making it more difficult for Palestinians to move between different Palestinian cities in the territories. Several Israeli Settler Highways even prohibit Palestinian usage.

3) Israeli Settler Belligerence and Disparate Legal Treatment: Israeli Settlers live under Israeli Civil Law even though their Palestinian Neighbors live under Israeli Martial Law. This creates a weird dynamic where Settlers who commit crimes are judged in Israel Proper in front a judge and Israeli jury. Palestinians who commit crimes are judged in the West Bank at a military tribunal presided over by an Israeli Army Judge. It creates incentives for Israeli Settler recklessness since Palestinians are likelier to face worse treatment for counterattacks than the Settlers for the original attacks. This is not to say that Palestinians are innocent in the bloody Settler-Palestinian clashes, but that the legal structure makes it easier for Israeli Settlers to provoke Palestinians without worrying about the consequences.

4) Abuse from Israeli Soldiers: In order to counter alleged threats in some areas of the West Bank, Israeli soldiers will commandeer inhabited Palestinian homes in the middle of the night in a procedure known as a “Straw Widow”. These incidents can be frightening and enraging to Palestinians, even though no Palestinians are killed or seriously injured in these attacks. There are also cases of violence between Israeli Soldiers and Palestinian Civilians on a daily basis. Some of this comes from Palestinians who rush at the soldiers using rocks and bricks as projectiles and some of this comes from soldiers who want to demonstrate macho-ness. Either way, the antagonism between the parties causes problems for Palestinians.

5) Evictions and Gentrification: This is an issue that often happens throughout the West Bank, but especially in East Jerusalem is that Palestinian homes are declared to be illegal constructions since they were never registered with an Ottoman, British, Jordanian, or Israeli building authority. Of course, this ignores that when these houses were likely built, in the Ottoman Period, there was not the degree of bureaucracy that would mark down all house construction. Since the Palestinian homes are marked as illegal constructions, it is permissible under Israeli law to destroy them. Often the net result is that a new house with Israeli Settler occupants shows up with minimal delay on the same land. A different, but parallel situation is also happening in Jerusalem as (1) prices are forcing Palestinians out of their homes due to inability to afford the areas (2) Israelis want to build new housing in undeveloped areas around Jerusalem that are officially part of the West Bank, and (3) Israeli Archaeology is going on in Palestinian East Jerusalem (especially the neighborhood of Silwan). This has pushed a not-insignificant number of Palestinians out of their homes and made a number of Palestinian neighborhoods.

Commentary on the Question:
Let us note that the question is specifically talking about the issues facing Palestinians at Israeli hands and completely ignore the Palestinian suffering at the hands or Palestinian Arab governments (like those of Hamas or within Palestinian-Authority-controlled Zone A in the West Bank) or at the hands of other Arab governments (like Jordan, Syria, Lebanon, and Egypt). It is likely that deaths perpetrated by these government (excluding incentivizing their people to commit suicide bombings and to act as human shields) is as high 24,000 deaths. The fact that Israel is usually discussed as repressing these people more than the Palestinians is indicative of myopic attentions.

Please read more about Palestinian suffering in other Arab countries in this Related Question: What are the events of the Arab-Palestinian Conflict?

Palestinian suffering at the hands of Arab countries and the Palestinian Authority is also discussed in depth by Palestinian Human Rights Advocate Bassem Eid in this article, among many others he has authored: Calling for an Awakening of Conscience: Palestinians Are Real People