Ik vind deze beter dan het vorige.

Here vinden means to think / consider / feel about something, not literally to locate something.

So Ik vind deze beter... means something like:

• I think this one is better
• I like this one better

Dutch often uses ik vind... to give an opinion:

• Ik vind het mooi. = I think it’s beautiful / I like it.
• Ik vind dit interessant. = I find this interesting.

So this is a very normal way to express a preference or judgment.

Deze and dit both mean this, but they depend on grammatical gender:

• deze → with de-words and with plurals
• dit → with singular het-words

Examples:

• de film → deze film / deze
• het boek → dit boek / dit

So deze suggests that the understood noun is either:

• a singular de-word, or
• a plural noun

In this sentence, it is being used as this one.

Yes. In Dutch, deze can be used as a pronoun, meaning this one or these, when the noun is clear from context.

For example:

• Welke jas wil je?
  Deze.
  = Which coat do you want? This one.

So in Ik vind deze beter..., deze means this one.

Yes. Beter is the comparative form of goed (good / well).

It is irregular:

• goed = good
• beter = better
• best = best

So you do not say goeder.

Examples:

• Dit boek is goed.
• Dit boek is beter dan dat boek.
• Dit is het beste boek.

In standard Dutch, dan is used after a comparative when you are saying one thing is more or less than another.

So:

• beter dan = better than
• groter dan = bigger than
• sneller dan = faster than

By contrast, als is used in equal comparisons:

• even goed als = as good as
• zo groot als = as big as

So here dan is the correct standard word because beter is a comparative.

Het vorige means the previous one.

Dutch often leaves out a repeated noun when it is obvious from context, just like English does with one:

• het vorige boek → het vorige
• de vorige film → de vorige

So vorige is functioning like previous one, with the noun understood rather than spoken.

This is a very good question.

Normally, if both parts refer to the same singular noun, you would expect them to match in gender:

• for a de-word: deze ... de vorige
• for a het-word: dit ... het vorige

So, if you are comparing two things of the same kind, many learners would expect:

• Ik vind deze beter dan de vorige.
  if the omitted noun is a de-word

or

• Ik vind dit beter dan het vorige.
  if the omitted noun is a het-word

As written, deze ... het vorige can sound a little unusual without context. It may be that the two words stand for different understood nouns, or that the example is just focusing on the structure. In normal usage, if both refer to the same singular thing, you usually make them match.

The word order is:

• Ik = subject
• vind = finite verb
• deze = object
• beter dan het vorige = what the speaker thinks about that object

A simple way to understand it is:

• I
  • find
    • this one
      • better than the previous one

Dutch main clauses normally put the finite verb in the second position, so vind comes right after Ik.

The structure with vinden often works like this:

• Ik vind het leuk.
• Ik vind deze beter.
• Ik vind dit interessant.

So beter is not randomly placed at the end; it is part of the opinion being expressed about deze.