because of the RAM or may be cores inside it
Shared internet gets slower more you have connected to it computers.
This could be for a couple of different reasons. Firstly it could be due to Firewall and Port settings which could be playing a part in the internet speed. Secondly, and probably more likely, your work laptop has a better network adaptor. New routers and new devices also support double frequency transmission of Wi-Fi signals (e.g. Samsung S4 and S5 along with other new devices) and this could be the case for you where your work laptop includes this new technology.
No unless your laptop has a slower processor in which case it will take longer to load on your laptop.
If your wireless access point will be connected to the same ISP and your wireless laptop will connect to this access point, there is no single problem with this configuration. Just the bandwith of your internet connection will be shared amongst the two computers instead of only one. Practically means, that is one computer will be downloading some large file, the other computer may experience slower internet connection. But it depends on how fast is your internet connection.
computers are slower
Yes, however, your internet speed will only be that of the G router which is comparably slower than that of an N router.
It depends on how much RAM each computer has, but sometimes notebooks can run a tad slower than desktop computers, depending on what you're doing on it. But if you're just on the internet or doing something simple like that, it shouldn't make much of a difference.
Yes, a wireless router can be used to share internet wirelessly regardless of where the internet is coming from. You should be aware though that a slow connection will only get slower when routed to multiple computers.
It depends on your computer and your internet. The worse internet the slower the worse computer and more slower.
your laptop will run slower then anything when you store documents movies music ect
it makes the interenet speed much slower
No they are a lot faster now.