Idling issue when warm + coughing under acceleration

Hi, hoping someone can help. 2 issues bugging me, possible connected but doubt it. Managed to get my mk1 GX 1.5 through winter and even MOT'D last week.

My annual mileage is 2000 mIles so not much at all.

I went through winter with a couple of issues, first being that I'd take the car on a long drive after warming and starting it using the choke etc. These drives would be on the motorway and ofcourse the car will warm up and I close the choke. Once I get to the right junction I want I normally stop at the lights and then the idle needle starts to jump down and idle under 1000 and just above 700  (setup to idle at 900 when warm). Yesterday after a long run and while sat at a junction it actually cut out and it's never gone so low and cut out. I've before used the choke to compensate but that's not a fix. Any ideas what my trouble could be? New carb went in last summer.

My 2nd issue is loss of power/coughing under acceleration. I thought this was an ignition system issue because it appeared in the cold months and seemed to have gone away until yesterday. I'm still thinking ignition, like maybe a bad condenser? Or even fuel pump but this  is a year old. Best solution is to go through the steps, im sure but thought I'd ask what this one could be too.

Help appreciated! 

What carb did you fitted and do you still have the original air box fitted to the carb?

Thanks for the response.

It's a Weber 36tlp and yes original air box.

Hi
Have you looked at condition of fuel filler neck and tank/fuel filter? had a similar problem after many things changed but in the wrong order it turned out to be a combination of things.If the carb has been set up correctly i would look at the things i have mentioned.No expert just drawing on my own experiences.Thanks.