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":