General
Trust your instinct on any interaction that starts unsolicited. Say no clearly if a shopkeeper follows you out. Walk with purpose — India reads uncertain body-language as an invitation to sell.
Women travellers
Solo female travel to India is entirely doable. Extra layers: modest dress in temple towns + smaller cities; women-only train compartments; the Blue Line metro in Delhi has a women-only carriage; avoid deserted after-dark walks. Meru Cabs + Uber-female-driver options in the metros.
Health
Water: bottled only. Ice: fine in decent restaurants + bars; ask if in doubt. Food: cooked-fresh is safer than salads; street food is fine at busy stalls (turnover = freshness). Immodium + Dukoral (bacterial pre-treatment) worth carrying.
Petty theft
Pickpocketing in crowded markets (Chandni Chowk, Colaba). Money-belt or front pocket. Don't leave anything on a restaurant table when you walk to the bathroom. Airport pickpocketing at the taxi rank is rare but happens — count bags before pulling away.