The concept of jihad is very misunderstood in the west. Its use also covers English terms like "struggle," "effort," and "perseverance."

JihadTo strive ; material resources ; or arms. Jihad is also used to refer to a war waged by the Muslims for the defense or advancement of Islam ; struggle. This can be any kind of striving in the way of God which involves either spiritual or personal effort - combat(ling) ; contending ; contention ; control(ing) ; fight(ing) ; strife ; striving ; struggle ; struggling

The root j-h-d is also used in words like "ijtihad" which is similar to "reasoning" by effort. Without going into the depths of how Arabic works, suffice it to say that words have a lot of associations that do not necessarily correspond nicely to words in Indo-European languages.

People have been "striving" in the name of Islam since the beginning. You can "jihad" for peace, which just means your working for peace. You can "jihad" for love, perhaps you are striving to maintain or pursue a relationship. It's really quite broad and the term existed long before Islam-- Islam just cemented the connotation of a "righteous effort."

arose from the Mongol invasions of the Middle East. Is there any truth in this?

As a short answer: no. But...

One thing that is sort of different about Islam and Christianity is that Islam places a lot of emphasis on communal relationship and the functioning of society as a whole. If Muslims are truly submitting to God, then society will be peaceful and happy. If society is not functioning this way, then the word "struggle" or "effort" (jihad) will inevitably get used a lot both as the internal effort to submit to God, and the external effort to make a safe and peaceful society.

So yes during the Mongol invasion, a lot of struggling was done. That word was probably used a lot. But it's happened with any large scale upheavals of society.

Wahhabi fundamentalists are those in the Gulf that the west supports. They helped the Saud family rise to power. They're the ones that impose veiling, separation of sexes, and traditional punishments such as lashings as a matter of law. They have experienced long lasting support from the west.

The current fundamentalist strain is concerned about are Salafists. And their ideology is rooted in the conflict with the Soviets in Afghanistan. They too were funded and supported by the west, though they came to completely reject anything that could be considered European-- anything from clothing, to forms of government. This is the ideology that has destroyed Syria.