Aerostart and its like are not good stuff to use on small engines, as you may realise. Difficult starting does indicate an engine problem, but it may be a simple one.
Your engine has the 'Pulsa-Jet' carby, with 'Choke-a-Matic' linkage operated slide choke.
As Unimog74 says, first check that the throttle control is fully extending the choke slide, at full throttle. Just pull the slide outwards, to see if it moves any further. Then check that the slide retracts fully, when the throttle is backed off.
If either condition isn't satisfied, first try adjusting the throttle cable. Loosen the cable clamp screw at the carby, slide the cable outer a little in the appropriate direction, and re-tighten. Check that the cutout switch, Item 3 in the diagram below, is still making contact when the throttle is fully closed.
If necessary, use pliers to
carefully bend the link at point 2 of this diagram, to adjust this:
![[Linked Image]](https://www.outdoorking-forum.com.au/forum/uploads/usergals/2014/12/full-5630-19150-pulsajet_choke_linkage.png)
The next step is setting the mixture, via the mixture screw. The factory setting is 1.5 turns out from the closed [fully clockwise] position; it should start and run well enough to complete the adjustment as Unimog74 has described. Run it for about 5 minutes, before doing the final adjustment.
By the way, if you can supply the Model, Type and Code numbers off the cowling [those numbers stamped near the carby], we can direct you to an owner manual and parts list for your engine. Can't quite make them out well enough, in your second pic.
