Q1: Does this card's When Digivolving effect still activate for my opponent's Security Digimon and give them -4000 DP when my opponent doesn't have any Digimon?
Yes, it does.
Lv.5 RizeGreymon EX4-009 R Ultimate | Vaccine | Cyborg [When Digivolving] 1 of your opponent's Digimon and all of your opponent's Security Digimon get -4000 DP for the turn. --- Inherited: [Your Turn] [Once Per Turn] When one of your red or yellow Tamers becomes suspended, 1 of your opponent's Digimon and all of your opponent's Security Digimon get -4000 DP for the turn.
Lv.5 RizeGreymon EX4-009 R Ultimate | Vaccine | Cyborg Digivolve: 3 from [GeoGreymon] [When Digivolving] 1 of your opponent's Digimon and all of your opponent's Security Digimon get -4000 DP for the turn. --- Inherited: [Your Turn] [Once Per Turn] When one of your red or yellow Tamers becomes suspended, 1 of your opponent's Digimon and all of your opponent's Security Digimon get -4000 DP for the turn.
Lv.5 RizeGreymon EX4-009 R Ultimate | Vaccine | Cyborg {{DigivolveFromNames|3|GeoGreymon}} [When Digivolving] 1 of your opponent's Digimon and all of your opponent's Security Digimon get -4000 DP for the turn. --- Inherited: [Your Turn] [Once Per Turn] When one of your {{Colour|red}} or {{Colour|yellow}} Tamers becomes suspended, 1 of your opponent's Digimon and all of your opponent's Security Digimon get -4000 DP for the turn.
Lv.5 ライズグレイモン EX4-009 R 完全体 | ワクチン種 | サイボーグ型 【進化時】このターンの間、相手のデジモン1体と相手のセキュリティデジモン全てをDP-4000。 --- Inherited: 【自分のターン】[ターンに1回]赤か黄の自分のテイマーがレストしたとき、このターンの間、相手のデジモン1体と相手のセキュリティデジモン全てをDP-4000。