Some states (about 13) will issue a drivers license or "non-drivers license" to a resident with no legal Immigration status. Many of these will accept a matricula consular as part of your identification, but I do not believe it is sufficient on its own.
Yes. In fact, most people who have a matricula consular are undocumented immigrants.
No. A matricula consular is not an acceptable proof of identy, residence or citizenship for the purpose of obtaining a United States Social Security card.
In many places, yes. The New York Public library specificly lists matricula consular on its list of acceptable id. One notable exception is Colorado, which has passed a state law explicitly prohibiting this.
Some counties/cities have set policies, but many do not. In general, it is up to the clerk issuing the marriage license to decide whether the ID presented is sufficient. Some clerks will require additional identification, such as a birth certificate. A foreign passport is better than a matricula consular, if you have both. Note that the presentation of identification is to prove identity only, not residency or citizenship. There is no residency or citizenship requirement to marry in any of the 50 states.
If this is the only ID you have, then it is better than nothing. You should invest in a (foreign) passport, however, and try to obtain a copy of your birth certificate. These are much better forms of ID. The one advantage that the matricula consular has is that it shows the address of your US residence.
Yes. There is no citizenship requirement for marriage in the US. A foreign passport should be enough for you to obtain a marriage license in any of the 50 US states. Showing a matricula consular with a US address may be a bad idea.
No
Yes.
No you cannot get a drivers license in Florida if you have had your license suspended in another state.
No
No
Yes. There is typically no citizenship requirement for obtaining a municipal ID. A foreign passport, foreign birth certificate and foreign matricula consular can be used, together with proof of de facto residence, to obtain a municipal ID.