I will revise the sentences that need revising and let somebody else comment on the question about finite/nonfinite verbs.
if you and your family are looking (fv) for a break away from all your troubles and maybe the cold and rainy weather, then come (fv) to Tenerife.
- If you and your family are looking for a break from your troubles or the cold and rainy weather, then come to Tenerife.
There is so much to do (nfv) lot's of fun like dolphin watching(nfv) .
- There are many fun things to do, like dolphin watching.
Note: lot's is not a word nor is it a contraction.
The beach is just a walk (nfv), through the resort
- The beach is just a short walk from the resort.
Note: walk is not usually used as a noun unless it is preceded by an adjective such as short or long.
It's beautiful sight.The most beautiful site you will see (fv).
So come down to where there is non-stop fun.So come (nfv) down where there is non-stop fun.