Learn Dutch: Hij morste het niet expres. - He did not spill it on purpose.

In Dutch, the negating word niet must be placed after a specific direct object (like the definite pronoun het). Here, it is positioned directly before the adverb expres, meaning it specifically negates the intention ("not on purpose") rather than the action of spilling.

Expres looks like the English word "express". Does it have the same meanings?

Only in a very narrow sense. In everyday Dutch, expres is an adverb exclusively meaning "on purpose" or "intentionally". You would not use it to describe an "express train" (which is a sneltrein) or the act of "expressing" a feeling (which is uitdrukken).

Is morste a regular or irregular verb?

It is a regular (weak) verb. The infinitive is morsen (to spill). Because the stem (mors) ends in s (a voiceless consonant found in the 't kofschip rule), it takes the -te ending in the simple past, making it morste.

Since this lesson is about vandaar dat, how could I connect this sentence to a vandaar dat clause?