When the gemara discusses that David did not sin, is it speaking of his being with Batsheva, or with any other sin? In Shm II, 24:10 has David admitting that he DID sin (and 70,000 people died as punishment). If he admits it, then how can we say (as in Melachim 1, 15:5) that the only sin was regarding Uriah?

Shalom, Thank you for your question. The Talmudic statement that “any one who says that King David sinned is mistaken” can be found in Shabbat 56a. Rashi there explains that it is referring to the sin with Bat Sheva before she received a divorce from her husband. As to the question from Melachim 1, 15:5 that states “because David did that which was right in the eyes of Hashem, and did not turn aside from anything that He commanded him all the days of his life, except only in the matter of Uriah the Hittite” – I was not able to find an answer in any of the classical commentaries. However, perhaps we can suggest that the sin you mention, of counting the people, whilst considered a sin, was in fact one of the things that “He commanded him” – see Shemuel II 24:1 “And the anger of Hashem was kindled again against Israel, and He incited David against them, saying, "Go, count Israel and Judah."” So, in counting the people David did sin, but it was (in some way) at the command of Hashem. I hope this helps. Blessings.