Apologies if this has been asked and answered before. I wasn't sure what to search for.

I am looking at London - Singapore. Cheapest option for Business on a OW airline is Qatar ticketed codeshare BA LHR - Doha and then Qatar to Singapore. Reversing on the way back.

Questions I have are
1 - I have only flown Qatar metal all the way before. I have a tight connection of 1hr 45. Last time I did this on Qatar operated flight from LHR is was no problem. Literally walked across the corridor. This time it will be a BA flight. Are the connections in the same terminal and equally smooth?
2 - On the way back I have about 9 hours in Doha. Again last time this was not an issue for me as I slept in the Al Mourjan lounge for most of it (which was a very good way of beating the jet lag). If I am flying out on a BA flight (but on a Qatar ticket) can I do the same or do I have to use the 'other' lounge?

Thanks in advance.