The number of phonemes in Czech and English is a simple matter of counting, and both languages have about 40 phonemes ("about" since phonemic status is a hypothesis dependent on method of analysis, not an self-evident observation). The reason for the difference in the nature of the writing systems is historical-sodicl. English has been written for longer, and has undergone more extensive sound changes, compared to Czech.
What you describe about English pronunciation is a fact about pronunciation (not spelling) and specifically it is about the nature of the phonetic system. There is actually something "difficult" about English, which relates to timing of articulations and its interaction with prosody, one example being the rule of aspiration (which I take to be what you are referring to in talking about the noise of "t") – p, t, k are pronounced aspirated or unaspirated, depending on position in the stress foot; vowels reduce depending on position in the foot.
The biggest challenge of English is figuring out (undoing and producing) the myriad contextual variants. Compared to Spanish (sorry, no experience with Czech) or even Russian, English has a very complicated phonetics because a small set of phonemes is turned into quite a number of phonetic segments. Moreover, language teachers for German, Czech, Spanish and so on are aware of the phonetic relations in their language (such as how b, d, g are pronounced in Spanich, how ch varies according to the previous vowel in German), but there is relatively little awareness of the range of contextual variants in English. Not to mention the fact that English is almost a language family, and we often need subtitles for speakers of an "extreme" accent.
