I'm trying to get ideas for my private practice (I don't want to call it my "hearth cult" because the people involved with the Longship have overused that term and now it feels cringe to use). I was hoping you could point me in the direction of any sagas that have some mention of how people might have worshipped at home or any prayers they might have used?
Unfortunately, there's actually surprisingly little to go on. Most of the sagas are very oriented toward public events, so the religious expressions they describe also tend to be equally public. However, there is a quite interesting paper by Luke John Murphy on the subject, and if nothing else you can skim it for the descriptions of the source material even if you're less interested in the comparative angle he takes.
Terry Gunnell's paper about indoor ritual space is probably a bit difficult to adapt for use nowadays but is very interesting and might spark some creative ideas.
One of my recent favorite books on Old Norse Religion, An Arena for Higher Powers by Olof Sundqvist, might also be helpful. It's big and dense, probably a lot more than what you're looking for right now, and is very much more about public religion, but is very thorough and some of that public religion stuff can probably be adapted for individual use. It's stealable as a PDF online.
I gave my own subjective answer to a question about private/individual heathen religious expression a little while back here: https://thorraborinn.tumblr.com/post/653078088152956928/how-does-one-worship-the-gods-in-private-im (my response starts at "As always"; my formatting doesn't tell you what's part of the ask).
I don't really know of any prayers but a common go-to is the "Heill Dagr, heilir Dags synir" ('Hail Day, hail sons of Day') stanzas from Sigrdrífumál. If you're up to writing something yourself, I think that would be great. I'd advise against overthinking it (do as I say, not as I do... overthinking it is why I don't really write poetry). A lot of the preserved poetry is extremely formally well-constructed but that doesn't mean that's all that people wrote or recited back in the day or that it's all that should be considered valuable, it's more that well-constructedness was a feature that made poems more likely to last (and professional poets had direct influence over what lasted) so there's heavy sampling bias. There's also no shortage of poetry and music by modern heathens like @poeticnorth.
