Yes, China can continue to build islands at least until an international agreement is unanimously reached concerning how to handle international waters. At this time China is within its right to build these islands, I believe, just as other countries sail on international waters or use them for fishing, oil drilling, and other purposes.
In an increasingly interconnected world, even the largest and most powerful nations are dependent on other countries for trade and security. The benefits the Chinese might hope to gain by building artificial islands in international waters are far outweighed by the disapproval of other countries, and the economic consequences of that disapproval.
China has been aggressively building military bases on islands built in disputed areas of the South China Sea. This should not be allowed, as it's illegal under international law and has caused an escalation of tensions in the region. China is the most powerful country in the region, but still needs to respect the sovereignty of the Philippines and its other neighbors.
No, China should stop building islands in the South China Sea. Multiple countries claim the same islands, and China's actions only inflame relations between those nations, making the potential for regional conflict and war to increase. The international community should sanction China in order to try to get it to stop building islands.