Q1: Do you treat the special digivolution requirements of "<Digivolve: 2 from Hawkmon>", written in the text for BT8-026 Halsemon, as an effect? Can BT8-026 Halsemon digivolve from Hawkmon in the breeding area?

Yes, BT8-026 Halsemon can digivolve from Hawkmon in the breeding area. Special digivolutions are a digivolution requirements with reference to special conditions, not effects. Therefore, special digivolution conditions can be fulfilled even in the breeding area. (From Card Rulings:BT8-012)

Data Sources

Official English Card Listworld.digimoncard.com

Lv.4 Halsemon      BT8-026  R
Armor Form | Free | Beast

<Armor Purge> (When this Digimon would be deleted, you may trash the top card of this Digimon to prevent that deletion.)[When Attacking] Delete 1 of your opponent's level 3 Digimon.

Official English (Asia) Card Listen.digimoncard.com

Lv.4 Halsemon      BT8-026  R
Armor Form | Free | Beast

Digivolve: 2 from [Hawkmon].<Armor Purge> (When this Digimon would be deleted, you may trash the top card of this Digimon to prevent that deletion.)[When Attacking] Delete 1 of your opponent's level 3 Digimon.

DCG Wikidigimoncardgame.fandom.com

Lv.4 Halsemon      BT8-026  R
Armor Form | Free | Beast

[Digivolve] [Hawkmon]: Cost 2

<Armor Purge>
[When Attacking] Delete 1 of your opponent's level 3 Digimon.

Official Japanese Card Listdigimoncard.com

Lv.4 ホルスモン      BT8-026  R
アーマー体 | フリー | 獣型

「ホークモン」から2≪アーマー解除≫(このデジモンが消滅するとき、このデジモンに重ねられているカードを上から1枚破棄することで、消滅しない)【アタック時】Lv.3の相手のデジモン1体を消滅させる。