The spells are underwhelming and lack upcasting ability (a must for most low-level Warlock spells). Shield of the People for example is basically the standard Shield spell with unnecessary description, uneccessary downsides, and trading Verbal components for Material (and why are you specifying saves vs Dispel Magic? That's redundant at best). Plus, I'm leery of the whole 'take damage to cast spells' thing in the first place unless the spells are definitively more potent than others of that level.
Mark of the Loyal is especially odd because you define it as a 7th-level spell and a Warrior/Warlock combo like you're describing likely won't ever get 7th-level spells.
If you're really going for a Warrior/Warlock combination, you might just punt the spells entirely and give them all Pact of the Blade (this basic 3rd-level Warlock feature straight-up outclasses your Loyal Blade spell in every way) plus maybe some original invocations. Just fluff it so they all have magical tattoos that fuel their Warlock powers.
Spoiler: Pact of the Blade for Reference
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You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it. You are proficient with it while you wield it. This weapon counts as magical for the purpose of overcoming resistance and immunity to non-magical attacks and damage. Your pact weapon disappears if it is more than 5 feet away from you for 1 minute or more. It also disappears if you use this feature again, if you dismiss the weapon (no action required), or if you die.
You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon. You perform the ritual over the course of 1 hour, which can be done during a short rest. You can then dismiss the weapon, shunting it into an extra-dimensional space, and it appears whenever you create your pact weapon thereafter. You can't affect an artifact or a sentient weapon in this way. The weapon ceases being your pact weapon if you die, if you perform the 1-hour ritual on a different weapon, or if you use a 1-hour ritual to break your bond to it. The weapon appears at your feet if it is in the extra-dimensional space when the bond breaks.
Invocations:
Pact of the Shield
Prerequisite: Pact of the Blade/<Homebrewed Warrior/Warlock Combo>, Cannot have Pact of Two Blades
You have a tattoo of a shield on your arm. When you summon your pact weapon in a form that can be wielded one-handed, you may use your Pact of the Blade feature to also form a shield in your other hand. You are proficient in this shield while you wield it and gain +2 to AC. You may also transform a magical shield into your pact shield using your Pact of the Blade feature without replacing your current pact weapon. All other restrictions of the Pact of the Blade feature still apply.
Pact of Two Blades
Prerequisite: Pact of the Blade/<Homebrewed Warrior/Warlock Combo>, Cannot have Pact of the Shield
You have a tattoo of crossed blades on your arm. When you summon your pact weapon in a form that can be wielded one-handed, you may use your Pact of the Blade feature to also form a second weapon in your other hand. This second weapon must have either the Light or Finesse property. You are proficient in this weapon while you wield it. You may also transform a magical weapon with the Light or Finesse property into your offhand pact weapon using your Pact of the Blade feature without replacing your main pact weapon. All other restrictions of the Pact of the Blade feature still apply.
Shield of the People
Prerequisite: Pact of the Blade/<Homebrewed Warrior/Warlock Combo>
You have a tattoo of a glowing shield on your arm. You may cast the Shield spell once without using a spell slot or requiring verbal components. You regain use of this feature after a long rest.
Sword Beam
Prerequisite: Pact of the Blade/<Homebrewed Warrior/Warlock Combo>
You have a tattoo of a glowing sword shooting a beam of light on your arm. Once per turn, when you make an attack with your pact weapon, you may make that attack with a range of 20/60 adding your Charisma modifier to your attack and damage rolls instead of your Strength modifier.