Learn Dutch: Wij meten het met behulp van technische apparatuur. - We measure it with the help of technical equipment.

Yes, you could say met technische apparatuur. The phrase met behulp van translates to "with the help of" or "by means of." It is slightly more formal and strongly emphasizes the instrumental role of the tools, whereas met is just a neutral "with."

Is behulp just another word for hulp?

They stem from the same concept, but behulp is almost exclusively used in the fixed expression met behulp van. For general "help" or "assistance" in everyday contexts, you must use hulp, such as in Bedankt voor je hulp.

Why does technisch get an -e added to the end here?

Because apparatuur is a de-word (de apparatuur). When an adjective comes directly before a noun that takes de, it gets the -e ending, regardless of whether the context is definite or indefinite.

Can I use a plural form if we are using multiple pieces of equipment?

No, apparatuur is an uncountable collective noun, exactly like "equipment" in English. If you need to refer to individual machines or devices and count them, you should use the word apparaat, which has the plural form apparaten.