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To answer the second part of your question, "DnD 3.5e" just means "3.5 Edition" and means exactly the same thing as "DnD 3.5". The first, more substantial, part of your question is answered by the question that Miniman has linked to.
More than the Basic Rules list of monsters, Wizards has released the 5e System Reference Document that has 200+ monsters encompassing nearly all of the classic D&D list of monsters. It is found from page 257 to 360 of the 5e SRD PDF.
You might well create very engaging adventures using only character races (men, elves, dwarves, etc.) and natural animals (for which you could improvise stats, if you even need them -- riding horses and farm animals don't really need them, most of the time). Even if you want monsters, you could create your own stats for creatures out of various myths ...
The Dungeon Master's Guide (DMG) does not contain any monsters. It does provide advice on how to create your own monsters, which is useful for creating your own adventures, but it's a lot of work to create a single monster, let alone all of the ones you require for a full adventure. However, the Monster Manual (MM) is not the only source of monsters. The DM ...
If you are interested in monster lore, rather than simply stats, I would strongly recommend getting Monster Manuals from 2nd edition AD&D. The 2nd edition Monster Manuals all include sections on Activity Cycles, Diet, Environment and Ecology of the various creatures presented. They also include information on what kind of organization they are likely ...
Not currently. However, all of the important rules (the ones you need to play with, and the ones you don't want to lug around a heavy hardcover dead tree for) are available as an SRD here and here in PDF format. This includes the experience tables for leveling, which weren't present in the 3rd and 3.5 SRDs. There's also an online 5th edition SRD ...
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