Is it a condition for seeking forgiveness (Istighfar) and performing the "Baqiyat Salihat" (enduring good deeds) to have the intention of achieving a specific matter, or is it permissible for the intention to encompass all the virtues and rewards associated with them?

Seeking forgiveness (Istighfar) is a request for the absolution of sins. It is not a condition for someone who says "Astaghfirullah (I seek forgiveness from Allah)" to intend the fulfillment of a specific wish. Whoever imposes such a condition has spoken about Allah without knowledge. Similarly, the enduring good deeds (al-Baqiyat al-Salihat) — "Subhan Allah (Glory be to Allah)," "Alhamdulillah (Praise be to Allah)," "La ilaha illa Allah (There is no god but Allah)," and "Allahu Akbar (Allah is the Greatest)" — are recited with the intention of drawing closer to Allah. It is not a condition for attaining their reward to recall their meanings, though recalling their meanings leads to a greater reward.