1997 Park Avenue issues

[slicklex]

I just got myself a 1997 park avenue, well while driving home I found some issues with the car.
1) The gas guage goes nuts from full to empty back to were it belongs and then it might stay there a while. However i noticed if you hit the fule info it will coincide with were the needle is reading at the time witch leaves me to believe it is not just the guage itself.
2) While driving it home cruising if you take your foot off the gas the speedometer jumps down in speed and starts going eratic and the transmission starts to I guess not know what gear it should be in and starts to rev up higher. If you leave your foot off for a few secs. it will return to the correct speed and you can go on. This car has the 4t65e transmission do these have a speed sensor on the trans?
3) With the key on there is a clicking noise kinda from the middle of the dash area. I think it might me a blend door motor for the climate control?

I just sold my 1994 lesabre with 144k on it. Never gave me a problem. I hope im not for it now. Im just looking to see if any of these are known problems. Thanks in advance

[Alibi]

97 is a bit too new for my blood, but I can hypothesize

1: Fuel sending unit (sensor). Part of the pump=not a fun job to replace
2: Assuming it is similar to a 4t60e, then it should have a speed sensor. As for the oddness in speed I'm not sure. Possibly the speed sensor or maybe a faulty TPS.
3: The clicking noise is probably a relay shutting. Is it one click or several?

It might not hurt to go to an autozone and see if it has any codes stored (I'd imagine the odd speed problem should have tripped something). Is the SES light on or has it been on before?