Responding to Fusion/Ritual Summons
In short, yes.

A trap like BTH is of speed 2, and a counter-trap like Solemn Strike is of speed 3. Both of these can be chained to the summoning of a monster. Quick play spells only reach a speed of 2, so regardless of the spell/monster effect used to achieve these Fusion/Ritual summons, both regular, continuous, and counter trap cards can be legally used in response.

As for your question on resolution, it wouldn't matter. Solemn strike negates the summon, so essentially, the card used to summon resolves, and then Solemn Strike prevents the monster from ever actually hitting the field. This is an attractive effect to a lot of players against certain decks because this prevents effects that happen when monsters are summoned, since the spell spell resolves, but the summoning does not.