Bamboo rods came with 2 tips because they were pretty easy to break. From what you are saying, one of the tip section has been broke and a new tip put on making it a shorter section.
If the rod has been kept in a fairly temperature and moisture stable place the glues that were used are probably still strong enough to fish it. Otherwise, you may have some issues when you start using it after it has been stored for a long period of time. Ferules and guides are easy repairs.
I would try a 6wt line to start and see how it loads, it would be middle of the road for most bamboo rods. I have one that casts a 7wt line and others that like the 5wt or 6wt lines. Bamboo is a slow action and will require getting used to casting if you have been fishing newer hi tech rods.
I bought a nice Horrocks Ibbotson Vernley 2 weeks ago at my great Uncles sale. He had promised me the rod a long time ago but never could find it. I was sitting with him watching the sale when I heard them call out Bamboo Rod. I won the bid and walked back over to give him crap about it. It was in the original tube and sock, still had the shrink wrap around the cork handle, in near mint condition albeit 70 years old. It is a 9 ft rod with 2 tips that are original length and casts well with a 5 wt line.
I have a couple other H I bamboo rods, a Herters, and a Heddon. I love to fish them, just have to be more careful with them. Make sure you dry them out good and wipe them off before you case them back up. I use a silicone base rod and gun cloth for that.