Q1: Can the Security effect of this card allow me to play a tamer card with a play cost of 4 or less that has "Liberator" as a trait?
Yes, it is possible. You can play a card as long as it has "Liberator" as a feature and has a play cost of 4 or less.
Q2: Can the Security effect of this card make digi-egg cards with "Liberator" as a trait play?
No, it cannot. Digi-egg cards cannot be played because they do not have a play cost.
Lv.4 Galemon ST18-08 SR Champion | Bird Dragon/LIBERATOR [Security] You may play 1 card with the [LIBERATOR] trait and a play cost of 4 or less from your hand or trash without paying the cost. <Vortex> (At the end of your turn, this Digimon may attack an opponent's Digimon. With this effect, it can attack the turn it was played.) --- Inherited: [Your Turn] This Digimon gets +2000 DP.
Lv.4 Galemon ST18-08 SR Champion | Data | Bird Dragon/LIBERATOR [Security] You may play 1 card with the [LIBERATOR] trait and a play cost of 4 or less from your hand or trash without paying the cost. <Vortex> (At the end of your turn, this Digimon may attack an opponent's Digimon. With this effect, it can attack the turn it was played.) --- Inherited: [Your Turn] This Digimon gets +2000 DP.
Lv.4 Galemon ST18-08 SR Champion | Data | Bird Dragon/LIBERATOR [Security] You may play 1 card with the [LIBERATOR] trait and a play cost of 4 or less from your hand or trash without paying the cost. <Vortex> --- Inherited: [Your Turn] This Digimon gets +2000 DP.
Lv.4 ゲイルモン ST18-08 SR 成熟期 | データ種 | 鳥竜型/リベレイター 【セキュリティ】自分の手札/トラッシュから、特徴に「リベレイター」を持つ登場コスト4以下のカード1枚をコストを支払わずに登場できる。 ≪ヴォルテクス≫(自分のターン終了時、このデジモンで相手のデジモンにアタックできる。この効果では、登場したターンでもアタックできる) --- Inherited: 【自分のターン】このデジモンをDP+2000。