[cwiggins]

Question 1: In the following sequences, is a double for penalty or takeout?
Question 2: If it is for takeout, at what level would it be for penalty?

Auction 1:
1♣ (P) 1NT (2♠)
where 1NT = 8-13 HCP balanced

Auction 2:
1♣ (P) 1♠ (2♦)
where 1S = 8+ HCP and 5+ long.

I looked in several Precision books, ("Precision in the 90s," "Precision Today," the old Precision books, "Power Precision") and could not find anything for either of these sequences.

In Auction 2, it feels that a double should be for penalty: presumably RHO has bid your secondary, or maybe even your primary, suit. The double might also be on a balanced hand with the right vulnerability conditions: perhaps white versus red and you hold something like:
♠xx
♥AQX
♦AQxx
♣KQxx

But Auction 1 doesn't feel as clear. For example, you would really like to make a negative double holding:
♠x
♥AQxx
♦Kxx
♣AKxxx
Also, many persons have switched to playing negative doubles after 1NT-(2♠). Does the same logic apply here?

[Free]

Since you're in a GF auction (I presume) you can use pass as penalty, and Dbl as takeout (or the other way around). No exceptions

[cwiggins]

So in strong club sequences, you always invert the meanings of pass and double?

This matches what Berkowitz-Cohen seem to do: see Berkowitz-Cohen Convention Card 2003 which says "pass/double inversion" without qualification.

On the other hand, Hamman-Soloway's system notes say that they play "Pass/double inversion in forcing high-level (3H+) situations." See Hamman-Soloway 2003 Bermuda Bowol Card

[Free]

Systems are always a matter of preference, I prefer this way