I'm trying to understand the following basic property of the restriction of scalars:

Given an absolutely simple algebraic groups $G$ defined over a number field $k$, are there at most finitely (up-to $k$-isomorphism) many absolutely simple algebraic groups $H$ defined over $k$ with $$Res_{k/\mathbb Q}G\cong_{\mathbb Q} Res_{k/\mathbb Q}H?$$ (i.e. their restrictions are isomorphic over $\mathbb Q$)

I understand that it follows that $G$ and $H$ are $k$-forms of each other and good understanding of the possible forms over the completions of $k$ should lead to an answer. This is because there is a theorem by Borel and Serre that establish the finiteness of forms that agree at all but finitely many completions.

Therefore my vague intuition is that the answer is yes, but I can't find a precise proof. Thinking about it also directed me to an even more basic question:

Given $G$ and $H$, two forms of each other (i.e., $G$ and $H$ both defined over $k$, and are isomorphic over the algebraic closure $\bar k$.) Is $G$ and $H$ isomorphic over $k_v$ for all but finitely many valuations $v$ of $k$?

I think that a positive answer to the latter should imply a positive answer to the former, but I think the latter might have a negative answer...

I'll be a happy if someone can shed some light about it and\or guide me to the relevant results in the literature. Thanks!