First, please forget about classfull networks, they are dead for decades now.
Having a /18 network is not recommended at all. As you pointed out, it is a very large broadcast domain that will cripple performance.
Apart broadcast, another problem is the number of MAC addresses a device can handle. This lead to two distinct issues:
Limit of switch MAC table size
Newest enterprise class device can handle 16 000 Mac address, but some are limited to 4096 MAC addresses. A consumer grade device like your linksys has generally a lower limit (a quick google search show 2000 but I didn't verified this).
So if you have too many devices, once the MAC table of a switch is full, it will flood the frames destined for the overflowing hosts, increasing the broadcast issue.
Limit of hosts ARP cache size
The ARP cache maintained but hosts can be pretty limited in size. I found a value of 265 for some edition of Windows.
When the cache is full, it is no more effective and ARP requests will dramatically increases.
I got 90K pcks with 50K of ARP packets
seems to confirm that this is actually your issue.
Additionally, I suppose (due to the size of the networks) that you have many Wireless clients, and SOHO devices are not designed to handle many clients. That may also explain the poor performance, but it's hard to say with the info provided.
is there any way to fix this?
You need to split your network in smaller, isolated (by VLAN) subnets, and use enterprise class access points (preferably WAVE2) to handle a great number of Wifi clients.