What might work in terms of your server stopping and starting is repairing your files (this essentially fixes any corrupt files which may be stopping/delaying your server). In order to do this, go to Minehut server control panel and click on the Danger Zone tab on the left, when you are in the Danger Zone, select Repair Files. When you've repaired your files, make sure to stop and then start your server. As for your other issue, make sure that your server is fully online (even if the status is displayed as "Online", give it 20 more seconds) and then join your server.
If my recommended solutions haven't worked, DM me on Discord (Clarifity#9353) or message me on the forums and I'll try to figure something out.