1. It really depends on what "moderate climber" means to you. There is absolutely nothing technical on the mountain, perhaps a few sections where putting a hand down for balance or putting feet onto rock. Rest assured though that it's not much more than a walk.
If you are reasonably fit then it's fine.
2. I've never done it in September but it's likely as good a time as any. You might even get lucky and not meet the local midge population. That (in my understanding) is at the back end of their peak season. You shouldn't experience any snow unless there is freak weather. Be prepared for a wee bit of ice though if the weather turns a bit brisk.
3. How long is a piece of string?
With regards to what weather you should look out for I guess I'd say the conditions that you are comfortable walking in at home with one caveat: this sounds higher than your normal altitude so bear in mind that low cloud means the summit (and possibly much more) will be covered by it.
I'm quite hesitant to say whether you should book a few days at the hotel. Sorry I'm not much help there.
Personally if it was me I'd probably keep an eye on various weather platforms, if they mostly agree then go for it.
I am possibly guilty of a bit of OCD when it comes to checking the weather but as I said if they all (or mostly) agree on good weather ...
I use (ready for it)
The MET office app, you can choose to view a summit forecast for Ben Lomond there as well as Rowardennan.
The MET office mountain weather forecast on the internet, you can choose an area (Southwest Highlands for Ben Lomond).
The MWIS app or website.
And (honestly it's good) the Norwegian MET office I think it's YR.NO
The windy.com app
Finally mountain-forecast.com
I DID warn you about that OCD
Another thing I would say is if weather conditions are good you can get an absolutely stunning view by not returning via the normal path, return via the Ptarmigan ridge for a great look along the loch. It's a bit rockier at the start but nothing technical. There is a relatively good path all the way. Worth looking into.
4. I could write a book here, uhm what to say... I carry too much but nothing is too much if you might use it one day
Make sure your weather proof clothing is good, trousers as well. Make sure you have warm clothing including hat and gloves.
Don't just take snacks, take food and a hot drink.
Personally I would carry over 1000 calories of food a hot flask and at least 1.5 litres of water.
I really am hesitant to go into all the stuff I carry because I don't want you spend money and likely (hopefully) never needing it.
However if you really want a list I'll provide one, be warned though
5. Oops I've already mentioned that but to reiterate yes it's worth it IF you have a view on the day.
If I remember correctly the most "scrambly" bit is the first drop off the summit towards the Ptarmigan ridge but once you're down that first bit it's really not much than a few "steppy" bits in places with a pretty good path.
Bear in mind that that "scrambly" bit only requires hands for balance, it's easy and safe.
If you get good weather then that ridge WILL vastly improve your experience on the mountain, I guarantee it.
6. I can't really think of anything else just now, if I think of anything I'll let you know, don't hesitate to ask if you can think of anything else.
Once others see your post I'm sure you'll get plenty of other responses which includes stuff I'll have missed.
Enjoy.