The loose stalk may be because the bakelite ring which holds it in
place has snapped, often due to overtightening the screw, take off the
steerring column shroud and you will see what i mean if that is the
problem. Usually it causes both stalks to go loose though.

What the Mini dealer said is pretty much right. You may see an
improvement by putting on a weber as you only have a 1.5" carb but a
1.75" SU would be a cheaper and easier upgrade. The difference between
a 1.75" and a weber would be slight. This is because the carb is not
the weak link in the chain so to speak. If you go for an all out super
fast expensive engine then you might need a weber, but not for this
state of tune. You can probably get a second hand carb off a metro or
another mini for about £30 or less

For a performance increase most people would advise a performance air
filter (K&N or similar), a better inlet manifold (one from an MG Metro
will do the job) and a better exhaust manifold and system. That will
put your engine at what is usually refered to as Stage 1. You can buy
stage 1 kits with all the above from Mini dealers for about £120ish
(maybe more now - I haven;t read a mini mag in ages)

Carb and stage 1 kit ay or may not give you about 20% more power which
will equate to about 10bhp. It will need to be set up corrctly on a
rolling road though. Increasing the airflow will alter the mixture
settings etc.

Second hand carb + stage1 + dyno tuning will probably cost you about
£200 in all. Less if you grab second hand or cheaper parts.

Stage 1 is probably the biggest increase you will get for your money
so enjoy it. After you have done that you are looking at heads and
cams etc which cost more and give you less power increases.

Cheers,
Dave