Hi

Upgrading from 32 to 64 (which actually means installing fresh since there is no upgrade path from 32 to 64) will probably give no issues.

There are could be strange pitfalls - I think some special security software are not always fast enough to follow the major trends among consumers.
I.e. there are electonic ID's client software used to identify yourself in government and authorities. Those could be limited to 32 bit versions.
I think the Flash-plugin for your web browser used to be limited to 32 bit browsers only, but I am not sure if that issue still applies.

Apart from that You should consider if this unit is a company owned one and then discuss with your IT department if this is an OK move.
If this is just your private unit and you do not have issues with Flash (if this is still a limitation) I see no major problems going to 64 bit OS.

You will be able to adress and use all your memory except for the part allocated to video.

The low amount of memory You see currently is simply caused by the limits of the OS architecture (32 bit).

Low memory messages are a bit odd however since 2. something GB memory should be anough for daily use.
If You are not using memory hungry applications maybe you should check your software (viruses, software problems) and possibly recover the unit.

BR

Tom