Kind of true... Your past hands relatively affect your future hands.
In Statistics, a lot of our study is on dependent and independent variables.
So, consider two cases:
1) Take the probability that your next hand is AA, GIVEN your previous hand was AA, call it X.
2) The probability your next hand is AA, call it Y.
One can see that X<Y. So yes your previous hands DO affect future outcomes depending on the statistical analysis you are performing.
Incorrect. Flip a coin, say it comes up heads. What bearing does that have on the next coin flip? Is it more likely to come up tails?
If you answer "yes" to the last question, you are not understanding statistical probability and causality.
If you're seriously interested in the topic (and it's a very good topic), check out a book called
The Poker Mindset - it's extremely good on this topic and (among other topics) discusses bad runs/downswings/tilt very much in line w OP's question.
Oh, and if you're interested (this part has absolutely nothing to do w poker), read a play called
Rosencrantz and Guildenstern are Dead, there's a really fun "joke" in there related to causality and coinflipping...