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:
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.
If you cannot make sure that your control circuit (e.g. microcontroller) can always keep DE deasserted unless it's actually transmitting (including startup, unprogrammed and similar conditions) you should by all means add a pulldown to DE to avoid tying up the bus. After all, it's about the worst thing that can happen to a RS-485 bus - no other device can communicate in this state. This is how I do it:
A pullup on /RE ensures that no spurious noise is received by the UART (and also allows putting the driver into a sleep mode if that matters). If your /RE and DE are connected together, pull that line in the "receive" direction (down).
Pullup values can vary if you have special requirements but 10K is standard for a digital signal not driven by an open drain.
For reference the TDA2822M datasheet can be found here.
Those capacitors are connected to the power supply pin (pin #2). They are acting as bypass capacitors. Bypass capacitors are designed to remove AC noise from the DC supply voltage. Since capacitors are a short at high frequencies, high frequency noise is shorted to ground while the DC supply voltage is passed.
You would not want to replace them with pull-down resistors. You don't want to pull down the supply voltage, and if you replaced them high frequency noise would be passed to the supply pin of the IC.