What would the life of a conscript be like before he is actually enrolled into the guard?
That will depend entirely on where he was conscripted from? Is he an agri-world farm boy or a hive ganger?
What does pilot training (e.g Thunderbolts, Lightnings, Valkyries) usually involve?
Presumably it's similar to pilot training these days - lectures, simulators, flights in a training aircraft etc
Also, what would the pilots normally be fighting?
Have a look at the Aeronautica Imperialis section of the Forge World site - that should give you a few ideas;
http://www.forgeworld.co.uk/Aeronautica-ImperialisAre female Lord Inquisitors known as Lady Inquisitors?
If they want - Inquisitor Lords are also known as Lord Inquisitors, High Inquisitors and probably other things too. Inquisitrix is sometimes used for a female Inquisitor. So she could be a Lady Inquisitor, Lady Inquisitrix, High Inquisitrix or some other variation depending on her exact position and personal preference.
What is the Conclave? (not this site, I'm referring to the one mentioned in Xenology)
From Lexicanum;
'Inquisitorial Conclaves can take two forms. The first is a gatherings called by an Inquisitor (if called by an Inquisitor Lord it is termed a "High Conclave") to discuss a particular subject. There are also more permanent regional Conclaves; these are federations of Inquisitors who watch over a particular area of Imperial space. The larger of these regional Conclaves may have resources such as ships, armies, fortresses, and libraries for the use of their members. Not all sectors of Imperial space are covered by a Conclave, and some areas are devoid of a permanent Inquisitorial presence. The head of each regional Conclave is normally an Inquisitor Lord, and is nominally appointed by the High Lords on Terra There are also Conclaves operating at the Segmentum level, again headed by an Inquisitor Lord.'
EDIT: Ooops, somehow I hadn't noticed Marco had already answered this - ah well...