You only need to supply the material that has a cost
As you quote
But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.
If the intent was to have you be unable to replace all of the components with a focus, it would say "a character must have all the components for the spell" -- but it does not, it just says "that specific component." A spellcasting focus can replace all the other components as normal.
Some spells do require you to have all material components on hand
However, some spells indicate that all of the material components have a cost. In this case, you must provide all of the components. For example, the MC of find familiar is:
10gp worth of charcoal, incense, and herbs that must be consumed by fire in a brass brazier
The charcoal, incense, and herbs must cost 10gp altogether, and they must be consumed by fire in a brass brazier. A spellcasting focus cannot substitute for any of the components here because all the consumable parts also cost money, and they specify the manner in which they must be consumed.
Divination is another example, which requires:
incense and a sacrificial offering appropriate to your religion, together worth at least 25 gp
Summary
In essence, the components you may not replace with a spellcasting focus are only those which have a gold cost, but all other materials can be substituted out as normal. However, some spells have material components which all share a cost, such as find familiar and divination. In these cases, you need to have all the components on hand.
No, because both spells use your action.
You need an action to cast Mage hand and another to control it.
Casting Time: 1 action […]
You can use your action to control the hand.
You also need an action to cast Summon Lesser (or Greater) Demons. Drawing the circle is only a part of that action.
As part of casting the spell, you can form a circle on the ground with the blood used as a material component.
Your mage hand wouldn't be dismissed, but it would just do nothing while you cast your Summon spell.
Best Answer
Yes
Summon Lesser Demon:
It does not say it has to be dead at the time of casting.
It does not even say it has to be dead at the time of collection, but I think that was the intent.
Balance Considerations
This spell is a bit weaker than Conjure Animals.
What arrives is on the same power level, as the summoned creatures have same CR. However with Conjure Animals you have more control over what you get, and what they do.
So for balance the components of Summon Lesser Demon should be less restrictive, not more.
For me this means whatever workaround or shortcut you can take you deserve it.