Sweden

Government website for immigration:

https://www.migrationsverket.se/en.html

https://www.government.se/government-agencies/the-swedish-migration-agency/

LGBT+ specific immigration programs (if available): I could not find any LGBT+ specific refugee programs through the Swedish government, but LGBT+ people can apply for asylum.
https://help.unhcr.org/netherlands/where-to-seek-help/lgbti/

Additional resources for LGBT+ asylum seekers:

UNHCR: https://help.unhcr.org/netherlands/where-to-seek-help/lgbti/

RFSL: https://www.rfsl.se/en/organisation/asylum-and-migration/vanliga-fraagor/

Swedish Government: https://www.government.se/government-policy/democracy-and-human-rights/measures-to-promote-lbtiq-persons-rights-and-opportunities/

Other sites pertaining to relocation/citizenship:
Sweden is part of the EU, and individuals with citizenship to a country within the EU may have additional avenues for immigration https://european-union.europa.eu/live-work-study/immigration-eu_en

Is same-sex marriage legal: yes
Are trans identities legally recognized and protected: yes

Are more than two genders legally recognized: there is a gender-neutral pronoun (“hen”), and there is social acceptance of non-binary identities, but there is no official X or third gender status on IDs to my knowledge

Is conversion therapy legal: currently yes, though there are efforts to potentially ban it in the future

Are there laws protecting LGBT+ people from discrimination: yes

other information: https://www.government.se/articles/2018/07/chronological-overview-of-lgbt-persons-rights-in-sweden/

See Equaldex for a chart with more specifics: https://www.equaldex.com/region/sweden

Are there any laws preventing discrimination based on other factors (e.g. religion, age, sex, ethnicity): yes

https://www.do.se/choose-language/english/discrimination-act-2008567