1

Both salutations are OK. You will not offend anyone.They will be happy to hear it especially from you as a foreigner.
cheers

2

Completely and totally fine.

3

Absolutely not an issue. If you are also looking for an alternative, some people will say 'Marhaban' to which the response is 'Ahlan'.

4

Absolutely fine and you'll often get a big smile (even from grumpy officials) for making the effort to say it.

5

Asalamu Aleykum is a traditional greeting - meaning merely Peace be upon you, its also used by Jewish people in their dialect and language and some christians too... It is however more associated with muslims since its a directive of the Prophet Mohammad to all muslims to always greet people with this phrase as there is 'barakat' like points in using this form of greeting. And it is still widely and commonly used by Muslims everywhere but particularly in the Arabic world - and not just be religious people..

Also if someone uses this greeting to you - you should reply .. Wa Aleykum Selam

If you want to have more 'points' you should reply ...

Wa Aleykum Selam wa Rahmatullah wa Barakatum

6

Yes it is very good. Speak clearly so they know what you are saying and you should hear in reply, wa Aleikum (and upon you). It is compulsory upon them to reply in kind, as good as you have given (but not to exceed that). Or if you are really lucky you may get, wa Aleikum Salam.

7

In Saudi Arabia, at any rate, it's considered gauche not to greet people or respond if greeted...even if you have no expectation of ever seeing them again in your entire life (e.g. people getting into an elevator with you in a random office building, or people who happen to be exiting a building when you are entering). Being Muslim or not has absolutely nothing whatsoever to do with the expectations of politeness.