Are there machines, where sizeof(char) != 1, or at least CHAR_BIT > 8?

It is always one in C99, section 6.5.3.4:

When applied to an operand that has
type char, unsigned char, or signed char, (or a qualified version thereof)
the result is 1.

Edit: not part of your question, but for interest from Harbison and Steele’s. C: A Reference Manual, Third Edition, Prentice Hall, 1991 (pre c99) p. 148:

A storage unit is taken to be the
amount of storage occupied by one
character; the size of an object of
type char is therefore 1.

Edit: In answer to your updated question, the following question and answer from Harbison and Steele is relevant (ibid, Ex. 4 of Ch. 6):

Is it allowable to have a C
implementation in which type char can
represent values ranging from
-2,147,483,648 through 2,147,483,647? If so, what would be sizeof(char)
under that implementation? What would
be the smallest and largest ranges of
type int?

Answer (ibid, p. 382):

It is permitted (if wasteful) for an
implementation to use 32 bits to
represent type char. Regardless of
the implementation, the value of
sizeof(char) is always 1.

While this does not specifically address a case where, say bytes are 8 bits and char are 4 of those bytes (actually impossible with the c99 definition, see below), the fact that sizeof(char) = 1 always is clear from the c99 standard and Harbison and Steele.

Edit: In fact (this is in response to your upd 2 question), as far as c99 is concerned sizeof(char) is in bytes, from section 6.5.3.4 again:

The sizeof operator yields the size
(in bytes) of its operand

so combined with the quotation above, bytes of 8 bits and char as 4 of those bytes is impossible: for c99 a byte is the same as a char.

In answer to your mention of the possibility of a 7 bit char: this is not possible in c99. According to section 5.2.4.2.1 of the standard the minimum is 8:

Their implementation-defined values shall be equal or greater [my emphasis] in magnitude to those shown, with the same sign.

— number of bits for smallest object that is not a bit-field (byte)

CHAR_BIT 8

— minimum value for an object of type signed char

SCHAR_MIN -127

— maximum value for an object of type signed char

SCHAR_MAX +127

— maximum value for an object of type unsigned char

UCHAR_MAX 255

— minimum value for an object of type char

CHAR_MIN see below

— maximum value for an object of type char

CHAR_MAX see below

[…]

If the value of an object of type char
is treated as a signed integer when
used in an expression, the value of
CHAR_MIN shall be the same as that of
SCHAR_MIN and the value of CHAR_MAX
shall be the same as that of
SCHAR_MAX. Otherwise, the value of
CHAR_MIN shall be 0 and the value of
CHAR_MAX shall be the same as that of
UCHAR_MAX. The value UCHAR_MAX
shall equal 2^CHAR_BIT − 1.