Should I remove things given to me by other groups from my home altar when I install the Gohonzon?

RKUK will not necessarily advise you to remove them.

The teachings of the Buddha are vast and boundless, and so Shakyamuni Buddha did not reject or proscribe other teachings. To the Buddha, the many deities and other beings that populated Brahmanism, the most influential religion in India at that time, were counted among the myriad living beings who could attain liberation by hearing his Dharma. He regarded all of these beings, who were believed to have supernatural powers as benevolent deities safeguarding the Buddha Dharma.

However, we will recommend you to put the Gohonzon at the centre of your home altar. You may have revered other buddhas such as Tathagata Medicine King. While every buddha is without a doubt venerable in and of themselves, the Lotus Sutra makes it clear as the ultimate truth that if we trace the buddhas back to their source, all originate in the Eternal Original Buddha Shakyamuni, and this determines our focus of devotion.