True, astral forms can only be affected by Mana spells. However, a Mana Barrier spell protects against all spells (see, for example, the section on Indirect Combat Spells, p. 204, SR4A).
As far as I can tell, this question is not answered specifically in RAW or FAQ. However, counterspelling is described as "the magician is actively “jamming” the mana around him" (p. 185, SR4A). That indicates to me that an astral magician should be able to counterspell just as he would in meat space, as counterspelling serves to interfere with the mystic link through which the spell acts.
Dispelling, however, is specified to be a same-plane thing: "Counterspelling also allows a magician to dispel a sustained or quickened spell, canceling its effect. The character must be on the same plane, must be able to perceive the spell she is targeting, and must use a Complex Action" (p. 185, SR4A).
Manifesting (p. 193, SR4A) does absolutely nothing, aside from making you visible and audible. It is not the same as Materialization, and it does not grant any ability to physically touch/attack/interact with anything.