Cannot shift to lowest gear - chain too short?
Yep, chain too short.

Yes, you can add some extra links in. The chain is new so you wont have links with different amounts of wear.

What I would suggest is splicing the left over links into the chain first. Then you will have a chain a few links shorter then original unshortened chain. Then size, re-cut and join it.

UPDATE: I was reminded by a comment that you cannot push out the link pin used to join the chain. You have to break the chain in a different place and push out a regular pin. Therefore, when you splice a section of links in you will have three link pins in the chain (the one you first joined the chain with and one on ether end of the spliced in section). This is very important. The link pins are of a slightly greater diameter than the regular pins and widen the hole through the outer plates when pushed in. A link pin installed where a link pin was pushed out will be substantially weaker.

I prefer Park Tool's recommended method to size the chain because it is far easier to perform (and safer). All you do is size the chain on the largest sprockets without threading the chain through the derailleur (because the chain would be pulled straight through the cage anyway). Without tension on the chain it's easier to hold in in place and mark the appropriate link.