Just for kicks, I will try to answer for my counties in PA.

Consitantly True or False?
1. A chain of assignments is determined by searching the county clerk indexes under the borrower name. True and False, in Franklin County, before the documents were imaged you had to physically look at the mortgage to see if an assignment stamp was on the mortgage.  They were not always indexed under borrower, mostly just the bank.  Now that they are imaging documents, assignments can be found by looking under the borrower's name, (assuming the name is indexed with the correct spelling).  In Fulton county I usually look under name and at the document just in case they missed indexing it.  They should always write it on the mortgage.
In Cumberland county, see Franklin.
2. Assignments to deeds of trust will  include the legal descripition .  We do not have deeds of trust, just mortgages, but assignments should have legals attached, but they do not always have them.
3. Fixture filings will  be indexed as Fixture Filings or Security Agreements.??? I think these are called UCCs or Secured Transactions in PA, not sure if they are the same.
4. Republic of Texas records prior to 1845 will be found in Austin.  N/A