Well, many questions...

Amira Yasmine El Haloui - Амира Ясмин Эль-Халуи (most probably)

Tanya - Таня. Actually it is diminutive from the name Татьяна (Tatiana). There is no tradition in Russia to use diminutives instead original names so you hardly can find name "Tanya" in official documents. According to the most accepted nowadays transliteration system Таня is Tanya. Though people can use different ways of transliteration.

No ideas why Czechs decided to use j for "short i" consonant sound. Poles apparently did that because they use letter "y" for another sound, which is equivalent to Russian "Ы".

Standard English James is normally transliterated as Джеймс. Not sure if I understood you correctly about your husband's name pronunciation.

Daniel - Дэниел or Дэниэл. There are Russian names of the same origin "Даниил"(Daniil) and "Данила"(Danila), both male, but they are considered not the same name as English Daniel.

Саша (Sasha) is the diminutive of either Александр (Aleksandr, male) or Александра (Aleksandra, female). If you like to transliterate "Xander", it should be Зандер or Сандер.

Миша (Misha) is the diminutive of Михаил (Mikhail, male only).