To answer point 4 first: ties and slurs are completely different things, although the notation looks similar. Ties always join notes at the same pitch, and indicate that the two written notes are played as a single long note. You will eventually see slurs over repeated notes at the same pitch, but don't worry about that yet.

The basic reason for writing ties is because some rhythms can't be written any other way. For example, you can't write a single note which starts in one bar, and ends in the middle of the following bar. You have to write two notes of the correct length to fill up the end of the first bar and the start of the second one, and tie them together.

Since you referenced a book for "absolute beginners," the following comments abut slurs are intentionally "the truth, but not the whole truth." The repertoire of the piano includes music written during the last 400 years or so, and during that time the meaning of musical notations has changed significantly. Trying to explain "everything" to a beginner would be confusing and overwhelming, rather than helpful.

Also, as you progress you will discover (or at least, you should discover) that piano music relies very much on creating illusions in the listener's mind - as an obvious example, since every note starts to decay in volume as soon as you have played it, playing a slow legato melody is literally impossible, but if you listen to a good performance of say Beethoven's Moonlight sonata (the first movement) that is what you think you are hearing, even though one long note of the "tune" may have become completely inaudible before the next note is played!

Slurs have different meanings for different instruments, and for singers. For example, for string instruments (violin, cello, etc) all the notes under a slur are played with one movement of the bow, but in some situations there can still be intentional gaps between the notes! In vocal music, slurs merely indicate that one syllable of the lyrics is sung to more than one note, and nothing more than that.

In piano music, you can make a rough distinction between "short" and "long" slurs.

"Short" slurs over 2 notes up to about 4 notes are the most informative. They mean that the notes should be joined together (legato), except for the last note which is played slightly shorter than its written value.

To be honest, Longer slurs don't mean very much in most piano music, except for a general indication to play legato, and to show the way the notes are grouped into phrases (which are often 4 bars long).

It is fairly common to see a long slur with short slurs "nested" under it. In that case, pay most attention to the short ones.

As you said, using the sustain pedal creates another set of possible options - but most likely your piano course won't introduce using the pedal until you can play fluently with both hands together. Synchronising both hands while they are doing "different things at the same time" is enough of a challenge at the start, without trying to your right foot do to something else different from either hand!

To answer point 4 first: ties and slurs are completely different things, although the notation looks similar. Ties always join notes at the same pitch, and indicate that the two written notes are played as a single long note. You will eventually see slurs over repeated notes at the same pitch, but don't worry about that yet.

The basic reason for writing ties is because some rhythms can't be written any other way. For example, you can't write a single note which starts in one bar, and ends in the middle of the following bar. You have to write two notes of the correct length to fill up the end of the first bar and the start of the second one, and tie them together.

Since you referenced a book for "absolute beginners," the following comments abut slurs are intentionally "the truth, but not the whole truth." The repertoire of the piano includes music written during the last 400 years or so, and during that time the meaning of musical notations has changed significantly. Trying to explain "everything" to a beginner would be confusing and overwhelming, rather than helpful.

Also, as you progress you will discover (or at least, you should discover) that piano music relies very much on creating illusions in the listener's mind - as an obvious example, since every note starts to decay in volume as soon as you have played it, playing a slow legato melody is literally impossible, but if you listen to a good performance of say Beethoven's Moonlight sonata (the first movement) that is what you think you are hearing, even though one long note of the "tune" may have become completely inaudible before the next note is played!

Slurs have different meanings for different instruments, and for singers. For example, for string instruments (violin, cello, etc) all the notes under a slur are played with one movement of the bow, but in some situations there can still be intentional gaps between the notes! In vocal music, slurs merely indicate that one syllable of the lyrics is sung to more than one note, and nothing more than that.

In piano music, you can make a rough distinction between "short" and "long" slurs.

"Short" slurs over 2 notes up to about 4 notes are the most informative. They mean that the notes should be joined together (legato), except for the last note which is played slightly shorter than its written value.

To be honest, Longer slurs don't mean very much in most piano music, except for a general indication to play legato, and to show the way the notes are grouped into phrases (which are often 4 bars long).

It is fairly common to see a long slur with short slurs "nested" under it. In that case, pay most attention to the short ones.

As you said, using the sustain pedal creates another set of possible options - but most likely your piano course won't introduce using the pedal until you can play fluently with both hands together. Synchronising both hands while they are doing "different things at the same time" is enough of a challenge at the start, without also using your right foot do to something different from either hand!