I am eager to know the guidelines to be followed for performing Sandhyavandanam during periods of ritual impurity due to birth or death (Janana, Marana Asaucham). Also, during long-distance travels extending day and night, can it be performed mentally/mantra-wise without taking a bath or using water? They say that during Asaucham periods, it should be done in a brief format (Sankraham) and Gayatri Japam can be chanted ten times. Are the rules the same or different for both Janana and Marana Asaucham? Is there any reference to this in the Shastras? I have made up my mind to perform it after knowing the details.

You yourself have mentioned in the third question that it should be done in a brief format and chanted 10 times; this applies to both Janana and Marana Asaucham periods. Furthermore, there is no custom of performing Anganyasa and Karanyasa. The rule is that the Japam and Pranayama mantras should not be uttered aloud, but should be recited mentally. During long-distance travels, Sandhyavandanam can be performed mantra-wise (mentally). However, the next day, upon reaching a place with water, the Sandhyavandanam missed the previous day must also be performed. The rules for Sandhyavandanam are identical for both Janana and Marana Asaucham. I do not understand what exactly you mean by asking for a reference.