It must be kept in mind that an Antimagic Field only suppresses a spell, it does not dispel it.

What I mean by that is that a spell is not destroyed when it passes through an Antimagic Field. Think of it as magical destructive interference localized on one spot. While the magic cast outside of the sphere interferes with the antimagic in the field, the effect of the spell can't be manifested. However, as soon as the magic passes that field the effects can reappear. This is why summons only vanish temporarily when an Antimagic Field crosses their paths and reappear instantly after.

A creature or object summoned or created by magic temporarily winks out of existence in the sphere. Such a creature instantly reappears once the space the creature occupied is no longer within the sphere.

Now let's check out the list in order:

1. Spellcaster inside the field. First and foremost, the description of Anitmagic Field explicitly states that spells cannot be cast from within the sphere.

   Within the sphere, spells can't be cast, summoned creatures disappear, and even magic items become mundane.

2. The line of effect passes through the sphere. In this case, the spell is not suppressed in any way, as neither the caster nor the target are in the field and the field does not act as cover from spells.

   Spells and other magical effects, such as Magic Missile and Charm Person, that target a creature or an object in the sphere have no effect on that target.

3. The spells passes through the field. This can be seen in two different ways: an AoE line or a magic projectile like Firebolt. Either way, the answer is the same, which is that it is suppressed while in the field and is no longer suppressed outside of it. For an AoE effect, the area of the spell that overlaps the field is suppressed, which means that a Lightning Bolt would stretch to the beginning of the field, then be suppressed, then reappear after the field as stated in the spell description. A Firebolt would travel in a straight line, also disappear as it passes through the field and reappear as it emerges from the other side.

   The area of another spell or magical effect, such as Fireball, can't extend into the sphere. If the sphere overlaps an area of magic, the part of the area that is covered by the sphere is suppressed. For example, the flames created by a Wall of Fire are suppressed within the sphere, creating a gap in the wall if the overlap is large enough.

4. A spell is cast on a point within the field. The answer is the same as the answer for (3). Although the "target" for the spell is a location within the sphere, the spell itself is not a targeted spell but an AoE spell. This behavior is the same as that of a Globe of Invulnerability.

Magic weapon will work against the lich

Regarding the last sentence specifically, magic weapon does not affect an area, it only affects a target (an object). Thus, this sentence has no relevance to this spell. The only purpose of this sentence is to exclude the globe from area of effect spells like fireball and the like.

Magic weapon affects one target: a nonmagical weapon that you touch. That weapon then becomes a +1 magic weapon for the duration. When you then try to use the weapon against the lich you are not affecting the lich with the spell, you are affecting them with the newly enhanced weapon. Thus, nothing about doing this would be blocked by globe of invulnerability. The same is true if you cast enlarge or invisibility or polymorph on yourself and moved into the globe to attack.

If globe of invulnerability did work against magic weapon it would lead to ridiculously powerful results such as creatures under the invisibility suddenly become visible since the spell "affects" the lich by way of making the PC impossible for them to see. Or that mirror image stops working because it "affects" the lich by making it hard for them to hit the PC. In essence it would make this spell on par with antimagic field, an 8th level spell.