Your canoe sounds like it's largely original, but the outside rail caps are almost certainly replacements. Morris rail caps are much more delicate than this and they're nicely tapered toward the ends. It is possible that your canoe had true outwales (see attached Morris catalog page for rail construction styles). If your stembands and canvas are original, the stembands should be attached to the canoe with rivets which require care to remove without damaging the band or the stem. Putting them back on is often done with screws, but some people re-rivet them.
Restoration - There are many people who will be happy to help you with restoration. See our Builder's and Suppliers Directory for sources of materials and expertise, plus the good people of these forums can offer very helpful advice and maybe even in-person help. Where are you located? Members of a local chapter can be an excellent resource. Finally, use the search function on these forums - there is a wealth of information here, available at the click of a mouse. Your concerns have been discussed here many times, and many people have provided a wealth of valuable information. Enjoy!
Briefly, if your question was about keeping the old canvas on the canoe, it is surely way past its useful life. Remove it along with the replacement outside caps. Paint can be stripped, either by yourself or a professional stripper. If you do it yourself, the strongest possible stripper (usually methylene chloride-based strippers like Strypeeze work well) is advisable. There have been many discussions about stripping here on the forums. Paint can be a bear - it can be much harder to remove; milkpaint is its own special beast (!). If the paint is on bare wood, it can be difficult to get it all of it of the wood grain. However, if it's on top of varnish, it can be extremely easy.
Hoping this is helpful,
Michael