I am by no means an expert...but I do know the one & only betta I have LOVES his 5 gal aquarium....so congrats on purchasing a great sized home for your future betta.
Again...no expert, but I also know that adding gravel and such from an established tank (seeding) to a new tank definitely speeds up the process of cycling....I have not seen spikes in the 2 tanks I did this with, even though I added a 2 fish to one, and hubby added I think 3 to another right off the bat. I have also done this with my Q tank when the previously used meds killed a lot of the bacteria and I saw a small nitrite spike (<.25) and it took care of it in less than 24 hours. So, yes, seeding is a good thing.....as for the salt in molly tank....I am not sure, but there are a couple of things you could check. First, research to see if salt treatment is indicated for Bettas for any diseases.....with some diseases, short term addition to a tank can help the fish recover. If you can use salt say for ICK on a betta, it would probably be okay because you can remove it with water changes by adding only freshwater and diluting the salt. Second...if you have any tanks without salt, or have friends that do....ask them to give you some seed material, then you know you would be safe. Third thing, you could probably rinse the gravel in fresh room temp tap water (treated for chlorine etc) to rinse most of the salt away. Gravel or filter media has much more of the beneficial bacteria you would be looking for than using straight tank water is my understanding...so that would be my choice. I don't know if just using the water would help much...but gravel, filter media, and decor work. I actually keep some small decorations inside of a cave structure in one tank that collects bacteria for me and is easy to throw into a filter bag for another tank. The kids wanted these little glow in the dark seashell shaped things that do nothing but get stuck in the gravel vac....so I found another use for them

. I hope that helps, if nothing else, it gives you some ideas on where to research next!