The trail from Popradske Pleso train stop (adjacent one to Strbske Pleso) to the Popradske Pleso lake and mountain hotel is just an asphalt road, so it could be done in a wheelchair. With 250 meters of height gain, it's certainly not an easy feat, but in terms of the road itself should be no problems. Also, just Strbske Pleso in itself is a very nice place too.

The Tatras are environment protection area, so you can't swim within the Tatras. You can swim outside of the Tatras like e.g. Czorsztyn Lake, but that isn't more interesting than any other lake so not much of an attraction.

If you plan on going to thr lake , check in the town you are staying in , as you could get a bus to the car parking area , it is a 2 or 3 km walk up to the lake , but you can get a horse carrage to take you up there , there is one cafe / bar / restaurant there , over looking the lake, nice place for lunch , but busy

Cable car takes around 20 mins to get there, if you buy there-and-back tickets the two rides are 2h apart which means you effectively have >~ 1.5 hour to spend near the top. You see some of the lakes in a valley below you although that's probably not the most spectacular of the places to look onto them due to distance. Depending on where you go, if it's in time when there is snow, a good idea to consider is taking cable car onto Kasprowy Wierch and walking down yourself - you can then visit very nice Czarny Staw Gąsienicowy lake, or if you're into a bit more walking, visit both it and Karb Pass which offers view onto it from above but from very close distance.

In Slovakia the airport is in Poprad, which is just few km from mountains. In Poland you can fly to Kraków and from this city take a bus to Zakopane (about 2 hours). On Polish side Zakopane is the most popular and the best place to stay if you want to hike in Tatra Mountains. On Slovakian side there are many villages and small towns, e.g. Tatranska Lomnica, Vysoke Tatry, Strbske Pleso, Zuberec.