So this question has two answers depending on the details. If British people came and did everything Jews did in the Middle East and history went in generally the same way, then yeah organizations like Hezbollah or Hamas would exist in pretty much the same way, and in that Hezbollah case they'd have probably organized Jewish volunteers to fight against British occupation (referring to their multiethnic volunteer force). This premise is of course historically unrealistic for many reasons, but it better captures the spirit of the question.

Now for the more historically plausible answer: If the Brits came and created a non-setter colony like they usually do, there'd of course be resistance that would start peaceful and turn armed, but it wouldn't be with the same intensity as what we see in Palestine and Lebanon today because Britain was in general a much milder colonizer than Israel is. The only place where the British did anything comparable to what Israel is doing was Ireland and you know what the Irish did about that.

Is it an anti Jewish organisation or an anti colonial organisation?

Like most paramilitary organizations in the region it's both, because Middle Eastern people generally don't think much beyond Jew = Zionist = enemy, but they're much more fundamentally an anti-colonial organization. The anti-Jewish part comes on later as the result of faulty reasoning. I mean let's face it, who even has the free time on their hands to create a paramilitary on par with a small nation's military because they hate Jews? Seeing people who happen to be Jews raping and murdering your period, pillaging and stealing your land and generally commiting atrocities is a much better motivator. This goes for Palestinian paramilitary organizations too, but for Hezbollah specifically remember that—while they've evolved a lot beyond their initial stage—their mandate was and still is to protect Lebanese land from aggression.

Yes.