The base plate appears to be grouted in, this is fine this will keep out water and oxygen from underneath, Don't worry about this. Your aim is keep it sealed. It shouldn't corrode.
The welds themselves are fine, corrosion appears mild and surface only.
The bulges on the steel are from impact damage, as most have pointed out
If you want to improve this, find a local welder to dress the beam back to shape, and clean up the weld.
Reason I'm suggesting you get a welder to do this is they'll have the right tools (grinder,pencil grinders to get in corners) for all of this should not take them longer than an hour including cleaning up, forget all the structural engineers nonsense.
It's a simple job, and the results they give you will certainly be worth it as it's prominent.
Paint wise, clean with methylated spirit , Paint the weld with a brush and use a roller for the rest, you'll get a decent finish. 2 coats of primer, let that cure, you may need to sand it to flatten out uneven spots. Prime again if needed then 2x coats top coat.should look a lot better.
"Johnstones" trade centre will colour match anything and is quality paint without stupid price tags.