Uppskeran verður meiri eftir því sem ræktunartíminn líður.

Eftir því sem is a fixed expression meaning as, in proportion as, or sometimes the more .... It introduces a clause that shows gradual change.

So here, it means that the harvest increases as the growing/cultivation period goes on.

On its own, því can be the dative form of það, but in this sentence it is best to treat eftir því sem as one whole expression.

In other words, you usually do not need to analyze því separately here. For learners, the safest approach is to memorize eftir því sem as a set phrase meaning as / the more that.

Verður is the 3rd person singular present tense of verða. With an adjective, verða often means become or get.

So uppskeran verður meiri means the harvest becomes greater or the harvest gets bigger. Depending on context, English may also translate it with a future sense, but grammatically the Icelandic form here is present tense.

Meiri is the comparative form meaning greater / more. It agrees with uppskeran, which is a feminine singular noun.

Because uppskeran is feminine singular nominative, the adjective also appears in the matching form: meiri. If the noun were neuter singular, you would expect meira instead.

Because uppskera means harvest, while uppskeran means the harvest.

Icelandic usually adds the definite article to the end of the noun instead of using a separate word like English the. So: uppskera = harvest
uppskeran = the harvest

Yes. Icelandic makes compound nouns very freely, and this is a very normal example.

Ræktunartíminn can be broken down like this: ræktun = cultivation / growing
tími = time / period
-inn = the definite article

So the whole word means something like the cultivation period or the growing period.

Yes, líða can mean to feel, as in Mér líður vel = I feel well. But it also has another common meaning: to pass or go by, especially with time.

In this sentence, ræktunartíminn líður means the cultivation period passes or the growing period goes on.

Because it is the subject of líður.

The clause ræktunartíminn líður is a normal finite clause meaning the cultivation period passes. Since ræktunartíminn is the subject, nominative case is exactly what you would expect.

Icelandic often uses the definite form in places where English may sound more general. Here, the sentence is talking about the harvest and the cultivation period as the relevant ones in the situation being discussed.

So even if English might sometimes say something more general like harvest or growing time, the Icelandic definite forms are very natural here.

Yes. A very common alternative is the því ... því ... pattern, for example:

Því lengur sem ræktunartíminn líður, því meiri verður uppskeran.

That means The longer the cultivation period goes on, the greater the harvest becomes. Your original sentence with eftir því sem is also completely natural; it is just a different way of expressing the same gradual relationship.