Can we buy shares from a foreign country's stock exchange?

Yes you can buy many markets are supported by local brokerages and Banks.

Here is a list copied from Phillips Securities However others too support most of these markets.

Asia Pacific

• Singapopore (SGX)
• Malaysia (BURSA)
• Hong Kong (HKEX)
• Thailand (SET)
• Indonesia (IDX)
• Philippines (PSE)
• Japan (TSE)
• Sri Lanka (CSE)
• South Korea (KRX)
• Australia (ASX)
• Taiwan (TWSE)

North America

• US (NYE, NYSE-MKT, NASDAQ)
• Canada (TSX)

Europe

• UK (LSE)
• Germany (FWB)
• France (Euronext Paris)
• Netherlands (Euronext Amsterdam)
• Portugal (Euronext Lisbon)
• Belgium (Euronext Brussels)
• Turkey (BIST)

Yes. As long as your broker allows you access to those stock exchanges. Check with your broker on this, each have different access to markets.