Which function do nicotinic receptors have in the periphery?
Short answer
1

Background
Nicotinic recepeptors (nAchRs) are widely distributed in the central and peripheral nervous system. Your question seems to focus on the peripheral nervous system. Taken from (Taylor, 2012):  

In the periphery, nAchRs are found in: 


Innervated skeletal muscle, especially postsynaptically in the motor end plate; 
The presynaptic nerve ending in some motor neurons to control Ach release; 
Ganglia at the postsynaptic dendrite and nerve cell bodies, and presynaptically to control Ach release.


Now in your answer the options 2 and 3 are incorrect, as muscarinic Ach receptors regulate gastric fluid secretion (Aihara, 2005) and contraction (Kitazawa et al., 2006). Given that nAchRs are excitatory receptors. In muscle cells, the binding of Ach leads to an opening of the associated ion channel, in turn producing a rapid increase in the cellular permeability of sodium and calcium ions, resulting in the depolarization and excitation of the muscle cell, thereby producing a muscular contraction (source: EMBL-EBI). This leaves only one opion left, namely 1). Since this was basically answering the question by exclusion, below Fig. 1 shows that answer 1) is indeed the correct one through a more positive approach - the top panel clrearly confirms that the sympathetic pathway deploys Acetylcholinergic neurons to stimulate its postganglionic adrenergic neurons.    


Fig. 1. Ach in the peripehral nervous system. source: Austin Community College 

References
- Ayhara, Gastroint, Liver Physiol (2005); 2886): G1199-207
- Kitazawa et al., Eur J Pharmacol (2007); 554(2-3): 212-22
- Taylor, Primer on the Autonomic Nervous System (3rd Ed. ( 2012}