Orchid - Can I remove the offshoot from the mother plant?

I have this orchid Phalaenopsis named Emperor of China. I have this plant since 6 yrs. ago and still look fine but hasnt blossomed this year. I am irritated when I see an offshoot from the main stem of the mother plant. Am wondering if I can remove the offshoot from the mother plant. At the same time, I notice a tiny spike between the 2 leaves. Can I remove the offshoot or should I wait?

Phalaenopsis orchid - Emperor of China, I got it since May 2015.

The phalaenopsis orchid to-date

An offshoot on the mother plant

A tiny spike coming out between the 2 leaves.

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