Hey Christian,
The answers to those questions are what separate the pro's from the rest of the bidders and you will have a tough time getting that information out of anyone that actually knows how to do it. We see people every month buy properties without knowing all the liens that apply and cringe knowing that they just bought a big headache.
1. Failing to perform an adequate lien search is the number 1 deal killer and biggest mistake most people make. There are several websites depending on the county that you are looking in that usually can help you research different types of liens (you are going to have to find these yourself). Some counties may require you to take a trip down to public records office. In general, keep an eye out for liens that don't get extinguished with a foreclosure such as child support, local property tax, mechanics liens, etc. Most liens like IRS, etc. can be removed when the ownership transfers but unless it goes through a formal foreclosure process you will have to try and negotiate them away. We typically have to look at four or more different websites and search by address AND variations of the owners name(s). This will get you about 90% of the liens, for the rest and a safety check work a deal with a friendly title company, even if you have to pay them for each search.
2. You have to dig and find the legal documents related. Most of the tax suit documents are in public records somewhere (court case, etc.) but there are often documents such as mortgages etc. that you may not be able to access. Some liens get slapped onto the property the day before the auction because people know the property is getting sold and they want their cut. We had a $75k IRS lien added to a $60k property hours before we bought it. We were able to get it removed but the IRS took almost a year to do it. No lien check would have caught that one.
3. County tax appraiser office. You have to be careful though, even if there is not a record of a homestead, if there is a house or USED to be a house, most title companies will default to homestead holding requirements regardless of the status which means much longer hold periods. Shop title companies to find one that reasonable wait periods.
4. County tax appraiser office. If there weren't back taxes there wouldn't be a tax lien so always get that information first. Liens could go back dozens of years and can get big quickly with penalties.
5. I have never heard of buying someone's "right of redemption". Usually tax auction properties are there because the owners are deceased and have no direct heirs to pay the taxes. You would have to get a quit-claim from the previous owner but my guess is that a title company would still make you wait the amount of time. They are the ones giving the title policy so it is their rules that matter. If the previous owner couldn't pay the taxes they won't buy back the property. The bigger threat is that another investor pays the owner to buy back the property, but at least you get your 25% profit. Just do NOT make any improvements to the property during the holding period, you will not get your money back on those.
Also be careful, in Texas the state says a 6 month redemption on non-homestead property but that doesn't mean anything. Depending on the city or county the property is in, the title company will default to the longest time required, usually 1 year. With a homestead or "possible" homestead it could be two years. We have had title companies say 3 years. No bases for it, was just what they felt comfortable with regardless of what the state said.
Stick with it, start small and learn your lessons up front. It will pay off in the end if you are diligent about always following your process.