@James Johnson the information from @Mike Cumbie about how CitiBank is likely to have policies that would seriously impeded your desire to buy this property is entirely accurate for most RE owned by CitiGroup. However, as you have seen, many of the properties in your area that Citi acquired from Allied Financial Services have not followed the Citibank policies. It is certainly possible, not probable, but possible that further exceptions to normal policy might be made -if that is the route you chose.
Mike is not quite accurate in stating that you have to be on the property five years to make a play. It is possible for you to tack the (7 year) period that your acting landlord has been in possession of the property on to your period of possession. There are benefits of not antagonizing your acting landlord. You may want to partner with him. If he can prove his possession for 7 years, then the two of you working together would have only 3 more years to qualify for adverse possession under Texas's 10 year statute -which applies whether any of you paid the taxes during those 10 years or not. However, if you want to stay there, do not let your residence go into property tax foreclosure. Someone must pay enough taxes to prevent the county from filing a foreclosure, because that public filing will bring all kinds of unwanted interest either from Citi or from other tax sale investors who will contact Citi. Also is some jurisdictions, once notice of impending tax foreclosure is filed, only the owner of record or a lien holder of record may be permitted to pay up the past due taxes.
Alternatively, if you do pay the more than two years of back taxes currently owed, you can still tack the acting landlord's possession onto yours and then it will only take you only 2 and a half more years of paying taxes and living at the property for you to claim it under the 5 year adverse possession statute that requires paying taxes. In that case, you paid all the taxes due for five years and lived there for 4 years and you would still need to tack on one year of your landlord's possession. You'd need proof (affidavit) of his possession and the nexus between you and him.
Mike is also correct in saying, "If anyone can make an adverse possession claim it would be the guy renting it out for 7 years" . However, if you stop paying rent, then you will move into the driver's seat. Since, your acting landlord does not appear to have ever paid the property taxes, he would not be able to use the 5 year statute and he can not claim adverse possession under the 10 year statute unless the full ten years has elapsed with him in possession. His possession ends, when you stop being his tenant.
Mike Cumbie is very likely correct that once you or someone else informs the right person at Citibank that Citi has ownership of this property, you could be told to leave.
"they will be removing you faster than you can imagine once they find out you are in there, especially without a lease"
It would be my guess that you'd be told to leave as well, but do not completely discount the possibility that someone with authority at Citi might realize they are better off with a paying tenant, than they are with a vacant property. The strange history of this property indicates a greater chance, though still not likely, that you'd be able to arrange a purchase or a rental with Citi. The fact that you have no rental agreement really won't matter. Citi would have to file an ejectment action to force you out whether you have a written rental agreement with the acting landlord or not.
Finally, CitiGroup's deep legal talent is reserved for their pressing needs. If you filed a quiet title action against them, the matter would be rated as to its importance and, if Citi decided it was even worth contesting, then a lawsuit over this property would be most probably be assigned to a very junior lawyer. The law would be in your favor. And it is hard for even the best lawyer to overcome the clear letter of the law. Let us know what you decide to do.