The example that I would like to use is:
Um welche Uhr es ist möglich für uns zu treffen am Dienstag (Morgen)?
Googling that question as well as using Google translate suggests that this is not the correct syntax.
If somebody can explain the grammar rules as well as the logic of formulating those kind of questions, it could be very helpful for me.
Your question is a little broad as there's not really an explicit question; I'll try to address a few issues in your sentence, though.
First, you'd ask "zu welcher (Uhr)Zeit" or "um welche (Uhr)Zeit". If you want to use the word Uhr, the question is "um wieviel Uhr".
Second, the verb has to come in second position here. Questions basically start with the verb, but the question word for when precedes this. I won't go into details here, but that's the reason why "um welche Uhrzeit" comes first.
So, there are certainly a lot of possibilities to ask this question. To my mind a very natural way is:
Um wieviel Uhr können wir uns am Dienstag treffen?
I'm having a hard time phrasing a question which combines all the elements that you tried to put into that sentence (i.e. "wann" + "ist es möglich" + "uns zu treffen"). At least I can't come up with something that sounds natural to me. I don't feel that the following sentence is natural
Um wieviel Uhr am Dienstag ist es möglich, um uns zu treffen?
I would rather go with a dass-clause. But then you'd drop "zu".
Um wieviel Uhr am Dienstag ist es möglich, dass wir uns treffen?
A natural way to use zu + infinitive that I can come up with right now, is something along this:
Wir sollten den Dienstag nutzen, um uns zu treffen. Um wieviel Uhr ist es möglich?
