Build a Finite Automaton with two states generating infinitely many strings.

Please build a Push down Automaton to generate all strings of the form $1^n{0}^n.$

Empty string is not generated. Please explain why $1110$ is not generated. Please

explain why $100$ is not generated.

Please, build a Context Free Grammar to generate all strings of the form $1^n{0}^n.$

Empty string is not generated. Please provide generation of $111000$

Please build a Push down Automaton to generate all strings of the form $1^{n+2}{0}^n$

where $n0$

Please build a Push down Automaton to generate all strings of the form $1^{2n}{0}^n$

where $n0$

Please build a Context Free Grammar to generate all strings of the form $1^n{0}^{2n}$

where $n0.$ Please provide generation of $111000000$

Please draw the pictures thank you.