Dtyjlui

How do you play two whole notes next two each other?
They're not stacked on top of each other but rather one is slightly right of the first.

It's in 4 4 time and so that means 1 whole note should take the entire bar.
So when should I play the second whole note?

There's also a tie that goes into the next bar which has the same two notes but they are now stacked on top of each other

These two notes are just one chord with 2 notes. You should play them simultaneously.

And in the next bar you hold the Sol, and change the Fa to Mi. It's not the same chord in that bar.

This is simply because we can not draw them stacked on top of each other, because they'd overlap. As you can see in this below image, this is how a chord with 4 continuous notes is drawn using Musescore 2:

They are not the same two notes both times; both bars have the G, but the F is in the first bar and E is in the second bar. This may be what is throwing you off.

To answer your question, you play the F and G at the same time, as a chord.
The reason they are not stacked vertically is that they would overlap and be more difficult to read.

In reference to the tie, you would hold down the G note over both bars, and change from F to E in the second bar.

This is a two voice part, the note G in the upper voice is actually a double whole note (or a "brevis"- breve am.) of 8 beats. In a 4/4 measure it can't be notated otherwise than 2 tied whole notes. The second voice is containing 2 whole notes (semi brevis) each of 4 beats.

In music, a double whole note (American), breve (international), or double note (Baker 1895, 133; Burrowes 1874, 41) is a note lasting two times as long as a whole note (or semibreve). ... In "perfect" rhythmic mode, the brevis was a third of a longa, or in "imperfect" mode, half a longa (Hoppin 1978,).

So they obviously have to be played on the first beat of the measure - otherwise they wouldn't fit together in two bars.

Two voices and chords with intervals of second (as well the intervals of unison) can't be notated in such a narrow system without apparent "overlapping" it seems to be also evident and has been explained elsewhere:

this picture may demonstrate it: (regarding the unison and the seconds)

(when there are half notes or shorter ones, in unison the note head of both voices can be merged in one head in seconds the heads will look in different directions when the are added at one same stem, while when used two stems the upper voice is notated on the left side stem up - and the lower voice looks to the right side, whereby the stems can be stuck or not be stuck.)