There is nothing but
The little boy jumped up and down.
There's no prepositional phrase in that.
If you have more sentences and I will put answers in Ask for details.
The first sentence, ‘My cat’s favorite pastime seems to be sleeping’.
A gerund is when a vets is used as a noun.
Future tip: gerunds most always end in ‘ing’.
Hope this helps.
These. it is demonstrating what the speaker is taking about