No they just don't weld in. This has been discussed regularly on the forum and I'm not going to go into why's and wherefores about it right now.
Rather lets just look at what has to be done.
B pillar - yes remove the small structural piece that goes up into the pillar. You can also leave the top of the old sill in the B pillar because the new sill does not extend up as high as the original. (doesn't matter if you have cut it out - it just means that filler pieces usually need to be bigger) You should be able to trim the old pillar fairly well to mate up to the new sill - even if you have cut more off than needed, it is not difficult to add small filler pieces to make up the difference. The welds are covered by the scuff plates anyway.
If the welds go higher than the scuff plates then you will have to use some filler to smooth up the welds.
C pillar - The fit needs to be obtained by slitting the new sill to match the dogleg profile and then manufacture filler pieces to suit.
A pillar - usually the new sill will need to be custom fitted to the front because the base of the A pillar is almost always rusted out and a completely new piece must be made before the sill is fitted. This new piece should be made in conjunction with the sill so that the best fit is obtained bearing in mind that the subframe bolt needs to be kept aligned.
The small amount of modification needed for the fitting of the sills is minor when compared with the remanufacture of the base of the A pillar, the front of the inner sill and the special crush tube inside the base of the A pillar.
If this is your first attempt at sill replacement then you need to take your time and ask lots of questions - especially about repairs to base of the A pillar - so well done so far.
Remember it always looks at its worst before any welding is done and you will be surprised at how much better it looks one the job is finished.
Ken McLean