Shouldn't be an issue, using right rod like E6010/13 or similar, will give good pentration. could even put a bevel on hanging eye.
For that gate a 2.5mm rod will be more than enough. Looking at how it was done, some STIKALL would be better.
Speaking as someone who has served their time to welding and spent many years welding to coded standard, arc or stick welding as it is known is the only way to go, I have used all the processes mentioned including Tig, Mig welding can be used on thicker sections but ideally it should be in a workshop so as the gas shield cannot be blown away by a slight wind, Gas welding is to some extent outdated but is still useful in some instances, this is an easy job for someone who can weld to a reasonable standard with a stick welding set either generator driven or if there is a power source that can withstand the load just use a plug in set, Phils welding set looks ideal. I would say for this to fail and rust in less than a year is not good, the gate and post should have been galvanised dipped after welding then painted, I would say the metal has never been galvanised, if it had been welded and treated correctly it would have lasted easily 15 + years and shown no sign of rust
It's ok, we've fixed it now with stixall...black stixall. Flatted down between applications, light coat of PVA, then 2 medium coats of zinsser 123, rubbed down with 80, then 120 grit, quick smear of SBR, flick over with a jappenese water stone then top coated with a propriatory black paint.
Cough... children, really. Anyhoo - any chance of photos of the broken pillar? Surely that's more relevant to this thread?