Yes. The reason they changed tigh to taigh was stop the t being pronounced as slender. But since it does not make any difference to the pronunciation of th, it was not necessary to change the spelling of oilthigh.
According to MacBain,
ollamh, a learned man, a doctor, so Irish, 0ld Irish [root, ollam, genitive ollaman ; from Irish oll, great (root pol, pel plê, full, fill].
The oil comes from Old Irish oll meaning 'great', so ollamh is a 'great man'. If that is the case then it is related to English full as the f would have been a p in Proto-Indo-European and the p would be lost in Proto-Celtic.
There are two issues here. One is the pronunciation of th. It does not sound like a normal t to me but I agree there is some sort of odd t-like sound at the beginning, so I would love an expert opinion on what is going on from someone who know the dialect.
As for the vowel, the vowel in this word is one of the most variable en Gaelic. There are theories as to why the word is different from Irish teach anyway. My guess is that the people living in Scotland had houses, and hence a word for them long before the Irish arrived, bringing their Gaelic. So what did the natives say? Well they spoke something like Welsh, and their word for a house would have been something like Modern Welsh tŷ. Even this word is subject to quite a lot of regional variation so I cannot tell you how to pronounce it exactly. But the the Irish arrive, bringing their word teach (which is actually taigh in some cases. The most important case is actually the locative, which you probably haven't heard of as it is obsolete, but it is the case you used to use when saying where something was - like you are 'at home', 'in the house'. In other words it was particularly common with places, such as your house. So basically the Irish heaped confusion upon the confusion that already existed, and what we are left with is a myriad ways to pronounce this word.
No. It is very confusing so join the club if you are confused. There are tons of discussion on this site to prove it.
Historically, the word for 'in' was an, related to English in, Welsh yn, French en etc. You will still hear/see this in very formal Gaelic and in set phrases such as an dochas 'in hope' i.e. 'hopefully'. But ann has been added to the beginning, for use before an indefinite noun, for no clear reason.
Ann an 'in' or 'in a'
Anns 'in' before an/na/a' 'the' and various other words that you will meet in due course.
You might be tempted to confuse ann with anns 'in' or ann 'there' but note that ann an can only mean 'in'. It cannot mean 'in the' or *'there the' (which is meaningless anyway).