This is well within the realm of DIY and you're not in any kind of danger, even if the whole post were gone you'd still have the railing top welded together and the torsional resistance of the monolithic baluster/top-and-bottom-rail assembly. You would not fall through without working hard to make that happen.
Ice damage isn't at play here. Rust always looks "swollen" because it is swollen. Damage from ice causes a split, it actually breaks the tube; the expansive force of ice is greater than the yeild strength of steel, it doesn't bend it or bulge it because the steel isn't ductile enough to accommodate the expansive pressures of ice at freezing temperatures.
The welds to the other parts of the railing provide ample strength. As it is, this is still plenty strong and you couldn't break it even beating it with a sledge hammer. Steel doesn't turn to glass like others here are scared about. You don't need to panic and replace this immediately out of fear and panic, keep calm and carry on as they say. Also, this looks like surface rust to me, and rust does look like it bulges because it is an expansion in a sense... and keep in mind the very basic point that water expands in the direction of the least resistance; with a hollow section member like a post that isn't sealed, the ice is going to break and unfrozen water will be forced upwards long before the steel starts to bend.
Responses to your questions:
Do I need to cut that piece out and have someone weld a repair or is it ok to leave as is?
Your choice, and no there is nothing mandating that you replace.
Should I put rust stop on it?
Your choice, but typical refinishing will be sufficient; stopping water getting/staying in is going to determine the fate of whether it continues to rust (this doesn't look like you salt so that's not a concern).
Since it's hollow should I seal the gaps in the cap above to prevent water getting in or does it need the ventilation to let it dry out?
It needs both and it needs a means for the water to drain.
You have a lot of sets of options and you will need to include a choice from each set:
- deal with the existing condition: do nothing and let it live many years until the whole thing is so rotten and unsightly that you can take your years of savings and replace the whole railing with one you like better; refinish it and keep the bulge, it's fine; full replacement; or, partial replacement.
- deal with water that gets in: fill the post; or, provide weeping.
- deal with water getting in: non-permanent seal, caulking or plug; permanent seal, welding; or, extend the cap.
Now you know:
- this is not a safety concern, and only needs to be dealt with if you decide the effort of remediating is less than how much you don't like the look.
- you can refinish, repair, or replace; is just a question of how easy and cheap you want to go.
- you are going to want to keep water from getting in and staying in, in order to prevent degradation to continue or affect a replacement in the same way.
To break down your options:
- to refinish: sand, prime, and paint.
- to fully replace: cut out the post free from the attached rails, remove the paver, cut the post so you have vertical working space, remove from the base, then replace everything if you have means to weld or hire a welder, and follow standard refinishing procedures for the given metal.
- to partially replace: if you know how to weld, you will know how to do this. For those folks without that know-how: This process is along the same lines as above, but just cut out the portion of the post you don't like. The work would include grinding the welds flush before finishing.
- note: you will need to "tie" into the finish on the adjacent railing components to blend old and new finish together.
- to fill the post: grout it, using the opening at the top.
- to provide weeping: drill a weep hole at the top of the paver and make it a big enough hole because you will want to grout it a little above the top of the paver so water that gets in doesn't pool at the bottom. Be warned, this will constantly drain rusty water over your pavers and permanently stain.
- to non-permanently seal: get a color matched exterior grade sealer that can accommodate the expansion/contraction of metals in it's cured state (so not acrylic or urethane); replace as needed, you should get a few years. To plug, find some rubber and shape to fit any openings; stuff it in there so it has some gently compression.
- to permanently seal: if you have means to weld, weld any holes shut. I'm assuming if you have means to weld you're not an idiot and understand when it's safe to weld something fully closed so you don't burst it and harm yourself; if you don't have means to weld, hire a welder to go this route.
- to extend the cap: either weld on a down turn, or hire someone to weld a down turn on that covers any holes; or, screw something that you've bent into shape from sheet metal to turn down over any holes.
Alternatively, you can take the point of view that isherwood suggested, there's nothing wrong with that point of view, and hire an engineering firm to come out and take x-rays of the crystalline structure of the post and make an empirical determination of the strength of the post to let you know if it is within your jurisdiction's threshold for lateral strength of resistance for railing safety then design a replacement and hire a certified welder and verify the strength of the welds with a special inspection.
If you want to verify, tap right there with a metal tool. It'll ring true if it's still solid, but bulged by ice. It'll sound dull and mushy if it's severely rusted. In the latter case it's in danger of breaking under the weight of a person and should be replaced ASAP.
The person who would break this would have to be one big boy, they would have to overwhelm the strength of the remaining steel, the welds from the adjacent railing components, and the strength of resistance of those components all tied together at the same moment. I wouldn't worry about this, but maybe you have some people in your life who can apply hundreds of thousands of pounds of force.
Some other notes:
- even sealed steel will draw in water through capillary action, don't seal it without giving a way for water to get out and also doing something to prevent pooling. Some light reading sources here, here, and here (laugh at the last one please).
- That steel decking is getting some rust, nothing to be worried about, but that is the structural part of your balcony so it is worth keeping an eye on and tracking. You may want to give some thought about the idea of replacing the sealant/grout between your pavers if it gets worse; but, this could just be from the cut ends of the decking corroding back when concrete was first poured or it could just be from water getting on the edge. Certainly nothing to lose sleep over.
- with your latest edit, you note the ceiling below is deteriorating; that is going to be from the lack of a drip edge and water rolling down the face and back underneath, soaking that edge year after year and getting sucked in between the finish and the base material, slowing separating the two.