Is it permissible to sit in any manner when sitting between the two prostrations and during the Tashahhud, such as extending one's legs or crossing them?

There is no specific posture required for sitting in the first or second tashahhud (definition); any manner of sitting is sufficient, whether it is cross-legged (tarabbu'an), extending both legs, or extending one of them. Imam An-Nawawi said: "There is no specific posture required for sitting in these positions for sufficiency; rather, however one sits is sufficient, whether one performs tawarruk, or iftirash, or extends his legs, or raises his knees, or one of them, or anything else." There is no difference between sitting between the two prostrations and sitting in the two tashahhuds in terms of sufficiency, regardless of the posture.