My advice, find someone else to buy from, sounds like he doesn't have a clue.
Whether it would make use of the RAM is nothing to do with the CPU unless it is a really old 32 bit processor, as far as i know all i3 nd above processors are capable of 64bit.
What would limit your memory is firstly the motherboard, again older mother boards had an 8gb limit, but as far as i know that hasn't been the case since the old intel Q-cores were replaced by the i-cores, so if it's an i3 it should be able to take at least 16gb, and secondly the operating system, there are 32bit and 63bit versions of windows, a 32bit windows install will only use 4gb of memory per application if i remember right, but that would be easy to rectify, just download the 64bit version of your windows operating system and install it, it should use the same license.
To be honest though, the main difference between an i3 and an i5 of the same generation is an i3 is dual core whereas the i5 is quad core, so can handle more processes at the same time, so i would choose the i5 over the i3 without hesitation, now choosing between i5 and i7 is a closer call because it depends on what you are using it for, an i5 is pretty much all you need for general use, you only really need the extras an i7 give you if you are doing high end rendering and video editing etc.
Also with regards to your existing memory and using it in the new machine, be aware that some motherboards will only use certain configurations of memory, and that depending on how old the board is you may be gated by the memory speed, for example you can get 3200mhz DDR4 RAM now, but some boards will only take up to 2600mhz DDR4 RAM, some board may only take DDR3 RAM, but again i think that's only if they're older boards like the old Q-core boards. Before trying your memory in a different board look up the make and model of the motherboard and you should be able to find the manufacturers documentation which will list the combination and types of memory it can handle.
Primary Desktop:
i7 7700,k NV1070 8GB, 16GB 3200mhz memory, 1x 2TB Hybrid, Win10.
Secondary Desktop:
i5 4760k, NV960 2GB, 16GB 2333mhz memory, 1x 2TB Hybrid, Win10.
Primary Laptop:
i5, NV1050 4GB, 8GB memory, 1x 1TB HDD, Win10.
Secondary Laptop:
i3, Intel 4000 series graphics, 6GB memory, 1x 500gb HDD, Win8.1.