Replacing capacitor from unworking TV with some other capatitors which has not the same value

I have only seen it done to increase voltage. On some power supply front-ends (AC/DC conversion) with a voltage doubler the capacitors are in parallel at low voltage and in series at high voltage. This works out well since for a constant power out the current is double at the lower voltage.

As you mention balancing resistors are required.

Yes, they should probably be okay.
However, since they are probably under a fair bit of stress (heat mainly) being part of a graphics card, ideally you would replace them with some high reliability/temperature rated versions.
Purchasing parts that have a datasheet from a "reputable" electronics supplier (Mouser, Digikey, Farnell, RS, Newark, etc) mean you can make a selection based on the ratings, and make it less likely that you will get some cheap and nasty caps.

To show the difference between typical aluminium electrolytic types (almost certainly the caps used on your card) here are a couple of datasheets from the same (reputable) manufacturer:

Standard 1000uF
High Reliability 1000uF

The parts you show should work at least for a while, but if you have the inclination, I would have a look and see if you can find some better parts that fit your board. The footprints for these parts are pretty standard, so it shouldn't be hard to come up with plenty of options. If you need any help deciding then just update your question.