Can I still use {Liliana of the Dark Realm}s +1 Ability even if there aren't any Swamps in my Deck anymore? ( in order to get her Loyalty up...)
Yes you can. You can activate it, you'll still have to search and shuffle but she will still get the +1. If you can see them it says so in the card rulings for her.
That's true, you can also not grab a swamp even if you are playing a mono black deck. Still search an shuffle but you can "fail to find" a swamp. You only can't fail to find on cards that say any card like {demonic tutor}