Can I go from a luer fitting to tubing?

Yes, there are adapters with luer on one side and a barb on the other. The barb is chosen by the inner diameter of the tubing and secured with a hose clamp under pressure.

What do male and female mean on a luer fitting?

The designation describes the cone, not the thread. Male carries the outer cone and is inserted into the counterpart, female carries the inner cone and receives it.

What is an extension adapter for?

It sits between syringe and needle and lengthens the path to the workpiece, which helps at poorly accessible spots. Bear in mind that every extension adds dead volume and flow resistance.

What is the difference between luer lock and luer slip?

Luer slip is the plain push fit: two parts with the same taper angle are pushed together and seal on the cone surfaces. Luer lock adds a thread to the cone and is screwed together. In dispensing, luer lock is the normal case, because a pushed-on needle can come off under pressure.

Which adapter do I need?

That is decided by the two ends to be joined. Note for each side whether an outer or an inner cone sits there. The words luer lock adapter alone are not enough to place an order.