Longitudinal bars: lap splices will prove ineffective unless lapped inside a proper mass of concrete, and not lapped in areas of high stress. For this reason, use full strength mechanical splices.
Welding bars is unlikely to be satisfactory unless you can ascertain the carbon equivalent (CE) of the steel. The carbon content of common steel reinforcing bar makes it difficult to weld, plus you must avoid heating the bar below the cover. AWS D1.4 describes the required procedures.
External confinement and shear reinforcement can be tricky, but applying a strut and tie analysis/design will assure the basic forces are covered. External flat bar ties could be used but they should be be grouted on to assure 100% contact. There aren't any good guidelines for bend radii and capacity after bending for this application, so you are on your own. Hot bending may or may not change the properties significantly from the specification (ASTM A36, etc.) I found that by the time you grind the corners, fabricate and install the ties, and provide new cover for fire protection, it was generally better to remove the old cover and damaged bars, replace the bars, and reinstall cover. This also removes any chloride-laden concrete near the bars.
Installing new ties which will provide proper capacity is tricky. Do not have closed ties bent, and then straighten and re-bend - the cold work of the steel will damage the bar (possibly cracking or breaking it.) Overlapping U-bars can be used, but that depends on the stress level in the bars and size of the bars and columns. The use of 135 hooks on ties requires clearance to seat the tails, do not cut the tails shorter than the code-required minimums, remove more concrete as required.
On a beams, I built stirrups using the slab on top, flat bars on bottom, and ductile all-thread on the sides, taking all of the shear into the all-thread. I'm not sure about the equivalent on a column.
Replacement cover should surround all exposed old and new bars, and proper consolidation is very important. New concrete should be very low shrinkage or shrinkage-compensating to reduce the likelihood that the cover with crack away. ICRI describes the proper surface preparation, including roughness and moisture conditioning. Consider use of lightweight aggregates in the new concrete to help reduce shrinkage due to loss of moisture during curing.