I. Can one with predominance of Rajas and Tamas worship Lord Vishnu?
Yes. Those with Rajasic and Tamasic Guna predominance can become devotees of Vishnu. Where Vishnu is considered the Supreme, though in his Saguna form as Vishnu he is sattvic, yet as the Supreme God he is the Lord of Maya and above these gunas which are in fact a product of Maya. ŚB 6.1. ...
If you consider gifting people to brāhmaṇas as if they were one's property, as slavery, then both Rāma and Bharata engaged in slavery.
In Vālmīki Rāmāyaṇa (Ayodhyā kāṇḍa), Rāma instructs Lakṣmaṇa to gift slave-girls (dāsī's) to a brāhmaṇa:
kausalyām ca yāaśīrbhir bhaktaḥ paryupatiṣṭhati |
ācāryaḥ taittirīyāṇām abhirūpaḥ ca vedavit || 2-32-15
tasya yānam ...
There's a verse in Srimad Bhagavatam that explains this directly.
kāma-lobhādayaś ca ye
ceta etair anāviddhaṁ
sthitaṁ sattve prasīdati
Translation: As soon as irrevocable loving service is established in
the heart, the effects of nature's modes of passion and ignorance,
such as lust, desire and hankering, disappear from the heart. ...