What is the maximum SMS message length?

Question 1

Messages are sent with the MAP MO- and MT-ForwardSM operations, whose payload length is limited by the constraints of the signaling protocol to precisely 140 octets (140 octets = 140 * 8 bits = 1120 bits).

Depending on which alphabet the subscriber has configured in the handset, this leads to the maximum individual short message sizes of 160 7-bit characters, 140 8-bit characters, or 70 16-bit characters.

As for your other question:

Is there is a difference between English and Spanish message lengths, since Spanish may contain Unicode characters?

No, there is no difference, as both English and Spanish are completely covered in the 8-bit Latin 1 character set.

Question 2

SMS allows for multiple SMS messages to be strung together (with the length of each reducing to allow for "joining" data). I have experience of sending messages of length of 612 characters (4 SMS messages) - there is a reduction of 7 characters per message segment. On the receiving system the parts may be received out of sequence, with the message only making sense once all parts have been received. The Clickatell API allows this, although their API guide at https://www.clickatell.com/downloads/http/Clickatell_HTTP.pdf recommends a practical maximum of 3 messages it allows up to 35 (see section 4.2.7). So (ignoring unicode for the moment) you can send a message of 35 * 153 = 5355 characters via the Clickatell API. If you are sending unicode characters (which the OP is not) the character count for a single message is 70, reduced by 7 characters for each segment in concatenated message or 63 * 35 = 2205 unicode characters.

Question 3

SMS messages can contain data of 140 bytes. However, SMS data is sent as a bitstream. This means if you are sending 7 bit ASCII, you can send 160 characters.