About characteristics of the cards

Do the abilities of cards affect the likelihood of winning / losing a campaign?

If we talk solely about the campaigns, no. Meaning that only the strength of your team is important (sum. of heroes’ strengths). You can compute it here:
Moreover, the strength of your team is displayed while you gather its cards in the Inventory (in app).

How is the strength of an individual hero/team calculated?

The formula is pretty simple:
Strength = Attack + Health.
For example: at the 1st level of the standard (not unique) card "Upir":
Health = 2740
Attack = 204
Strength = 2740 + 204 = 2944.

How fast energy (meat) is being restored?

1 unit / 10 mins
Meaning that you gain 6 pieces every hour.