1. A Srivaishnava is a devotee of Vishnu; one who behaves to the please Bhagavan acquires the eligibility to become a Srivaishnava, otherwise one cannot be a complete Srivaishnava based on this aspect.
There is no stipulation that only Smarthas or Vaishnavas are prohibited from eating onion, or garlic. It is not a sattvic food. Bhagavan had preached that everyone must respect and follow what the scriptures have ordained so that they become his devotees. Vaishnavism is complete if such food is avoided.
Even if one consumes them due to family compulsions, it is considered a sin as the scriptures have ordained them not to consume. It is not only for Srivaishnava-s but common to all.
2. A Srivaishnava must wear Tulasi garland. The garland is of different types, our elders do not wear an un-consecrated garland, but people of other traditions do so. Our Azhwars, Acharya sampradayam accept Tulasi garlands that have undergone prathishtai. One should observe rules like not wearing them during asaucham, one can wear them upon the advice from elders.