OK. I'll bite. Sorry if I make assumptions not intended.
$20K for a 30% interest in a property worth $120K. $20K of $120K = 17%, not 30%. So, your consideration for past rent amounts to 13%, or $15.6K. Unlikely even a benevolent uncle would be interested. Your past rent is water under the bridge. You agreed to the rent, and received whatever benefit from renting the space. I think it a little much, even after all the years, to ask that it now be considered for such a chunk of equity.
You've already indicated a difference between you as tenant, and your uncle as landlord, in willingness to do needed maintenance (the roof). Do you really want to be a junior partner in a property where you and your senior partner differ on what needs to be done and when? In the end, his share rules.
In order for this to work, and your $20K to be considered in the purchase of the 30% equity, you would, IMHO, have to turn over the $20K to your uncle, and then the business/partnership would get the repairs done. You might not get the control over the repairs you expect, or even how much he would spend in total. I'm sure a good lawer could structure the deal so that the funds were held in escrow for the repairs.
I think your tax question is very relevant. I'm not sure you could continue paying rent on a property you hold an interest in. I imagine there are a lot of legal details that need to be ironed out so this could work, if the two of you do come to any agreement.
You make no mention of how much of the total space you rent, or the type of building it is (I'm assuming commercial from your description). Also, whether the buidling is owned by himself, or through a LLC, whether it's profitable and whether the nephew has been getting a family discount on the rents for all these years. So, in a sense, I'm winging this with little information. But, I can't imagine he'd give up a 30% stake for 17% cash that goes right back into the property, possibly lose your rent and split the remaining profits 70/30. Sorry if I assumed things not mentioned or intended, but there are a lot of considerations.