"Connections" ?
You've got a couple of problems - and, I'm not sure exactly where you are looking for help. What we did a few years ago was the following: Resedintial house, basement was about 25 feet across with 2x 3" pipe columns that the contractor wanted to open up into a single room. Apparently, similar to your situation. One wall of the basement was open to access from the side.
We cut a hole in that wall high enough and large enough to slide the beam directly in from the outside - don't have sizes, but I believe it was a W12 or W10 x ???, standard A36 grade. Obviously, YOU have to size it based on span and loads. We cut the beam to length outside the house (no flame-burning and clear grinding inside!). The existing pipe columns were left in place until the beam was slid into the basement, lifted up manually into final position, and on its final supports. We needed 6x people to lift, assume each can only lift 150 lbs over their head if on good supports or scaffolding. Otherwise, plan on several jacks underneath - obviously, you can't use any crane through the roof. The contractor did not want anything settleing, so he jacked up the old floor with temporary verticals very very slightly to get the load off of the old columns and to allow the new beam to move into place just slightly "above" its final elevation.
Once up against the floor joists, we supported the W10 beam at each end with 2x vertical columns that were end turn bolted against the existing basement walls (either brick or CME - I do not remember - and to their own floorplates on the old concrete. Once the new beam was in place and jacked up firmly against the old joists, (since the old joists were actually lifted a little bit ("un-sagged" may be a better word)), the 2x pipe columns were felt to be "loose" and could be simply pulled out since the temporary verticals were carrying the load of the floor above. With the new beam in place and secure at both ends, the temporary jacks were relaxed that little bit they had lifted the floor (1/16" perhaps) so the old joists were lowered and transferred their weight to the new beam.
We had two or three old joists that needed to be smoothed (sanded off) so they touched the new beam evenly with the rest: This is because the new beam was "perfectly flat and dead level" on top and the old wood was "not so perfectly flat" and "not so perfectly level" across its average bottom with these few being too low or slightly twisted by the old nails. 8<) The hand grinder we used to smooth the W10 beam was more than adequate to trim the 2x12 where required in only a few seconds. Old joists that were too high to touch the new beam were shimmed with wood shims firmly wedged in place.
I do not remember how the new columns were attached to the new beam. We are in a no-seismic zone. Anything that works in your case will be adequate.
The new end columns were covered by 2x4's and sheetrock panels to match the rest of the new basement's interior walls.
Remember to plan the holes in the basement walls for lifting the new beam up and sliding it in safely, and remember to get enough people in the right places to do that lifting safely.
if you can't get sideways access into the basement, I'm not sure how you can get the new beam into position. I most definitely don't recommend cutting it and re-splicing it by welding inside the basement unless you have a very, very skilled welder who can work in remote sites safely.
