What is Reddit's opinion of The Model 1903 Springfield Rifle and its Variations, 4th Revised Edition?
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OP I would suggest picking up the book listed below if you are interested in learning more about the rifle.

I recently picked up a 1903a3 and have found this book to be very useful

https://www.amazon.com/dp/1882391306/ref=cm_sw_r_apa_i_rszkFbS17RKEE

Buy a book... if you want the rifle to be "correct", there's way more detail to that answer than can easily be described in a single comment.

Joe Poyer's book on the 1903 will address your questions and it's only 25 bucks on Amazon

I would encourage you to buy a book on the subject if you're curious to learn a lot more. Poyer's book on the subject is cheap and has a lot of info in it: https://www.amazon.com/Model-Springfield-Rifle-Variations-Revised/dp/1882391306

I'll have to pull mine out to answer these questions with any certainty.

Check the FAQ in the sub, in particular this section which I compiled. There's some free resources online that I've linked.

I actually made a post specifically on Remington 1903 rifles with some links to details.

If you want more details, Joe Poyer's book The Model 1903 Springfield and its Variations, 4th Revised Edition is probably the most affordable. William Brophy's book The Springfield 1903 Rifles: The illustrated, documented story of the design, development, and production of all the models, appendages, and accessories is generally considered the bible on the topic of the 1903, though it's significantly more expensive.

You could also post pictures with specific questions on this sub or /r/milsurp.

You really ought to buy a reference book if you're trying to assemble a "correct" 1903.

Poyer's book is cheap and good enough.

How much money do you want to spend and how correct do you want it to be? I'd suggest you Buy a book and do some research before doing anything.

This book is decent

or if you want more detail

This book

Beyond that, you've not provided nearly enough information to really give you much advise. It may be a simple stock swap or it may be a rifle that's not worth the time/effort to fix.