What are the starting and ending addresses if the DS register contains 1A30H in real mode addressing scheme?

The starting and ending addresses if the DS register contains 1A30H are 1A300H and 2A2FFH. The effective address range is 0H to FFFFH, and you simply add that to the segment register times 16 (left shifted 4).

The 8086/8088 only operates in real mode. You don't have any other (protected) modes until you get to the 80286 and higher processors.