Nightfires :
1. Would the gtx 760 fit in the dell inspiron 620 mini-tower? 2. Would the temps be fine in the case? 3. Would you recommend to get the 750 ti or buy the gtx 760 and new psu? 4. If you think buying the new gpu would be best, what psu should i buy and also what 8 gb ram (4x2) should i buy? 5. Are you sure that my default 300 watt dell psu would work with that pny 750 ti if i got that? And not mess up? Thank you

i need some help
1) I'm not personally familiar with the insides of the 620. But if this is what yours looks like inside:
http://i.ytimg.com/vi/4JEgMuSxfkU/maxresdefault.jpg
...you will need to measure the distance from the rear expansion slot cover to the drive cage to see how much room you have. Then compare that to the stated length of the GTX 760 you choose.
2) The temps will be fine with most cards. It will get warm, but with the top mount PSU and the small rear fan removing heat, it should be OK. An open, vented top would be preferred. If possible, install a front fan to force some air into the case. As big as one that will fit the mountings. Usually a 120mm.
3) If this is the same nameplate specs as on your PSU:
http://data.stuartconnections.com/object/image?p=10103&i=2
...you can squeak by with the GTX 750 Ti. I have used one on a similarly rated PSU with no issues. Your i3 is a pretty low wattage CPU. Of course, it would be best to buy a new PSU and move to the GTX 760. But if you go with the 750 Ti and the old PSU, it will be OK.
4) If you decide to upgrade to the GTX 760, Nvidia recommends a 500W minimum PSU w/2 x 6 pin connectors:
http://www.geforce.com/hardware/desktop-gpus/geforce-gtx-760/specifications
This would be a decent low cost 500W PSU:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817438012
A bit better would be:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817207030
But keep in mind, these are all designed for bottom mount. So the cables will be a bit long when the PSU is mounted on top. You'll have to be ingenious in figuring out a way to tie them out of the way to prevent blocked air flow.
What are the specs of your memory now?
5) Pretty sure.