i$.$ I can't create visual flowcharts, but I can describe a structured approach:

$1.$ Initialize R$1$ to $0.$

$2.$ Set a counter $($let$\text{'}$s say R$2)$ to $0.$

$3.$ Load a number from memory location $(0$x$3100+$ R$2)$ into a temporary register $($R$3).$

$4.$ Add the value in R$3$ to the content of R$1.$

$5.$ Increment R$2.$

$6.$ Repeat steps $3-5$ until R$2$ reaches $10.$

ii$.$ LC$-3$ ISA instructions:

$-$ Initialize R$1$: $`$AND R$1,$ R$1,$ #$0`$

$-$ Set counter R$2$ to $0$: $`$LD R$2,$ #$0`$

$-$ Load number from memory to R$3$: $`$LD R$3,0$x$3100($R$2)`$

$-$ Add R$3$ to R$1$: $`$ADD R$1,$ R$1,$ R$3`$

$-$ Increment R$2$: $`$ADD R$2,$ R$2,$ #$1`$

$-$ Repeat using a loop instruction like $`$BRnzp$`$

iii. IC$-3$ assembly language program:

$```$assembly

; Initialize R$1$

AND R$1,$ R$1,$ #$0$

; Set counter R$2$ to $0$

LD R$2,$ #$0$

LOOP LD R$3,0$x$3100($R$2)$ ; Load number from memory to R$3$

ADD R$1,$ R$1,$ R$3$ ; Add R$3$ to R$1$

ADD R$2,$ R$2,$ #$1$ ; Increment R$2$

BRnzp LOOP ; Repeat until R$2$ reaches $10$

$```$

iv$.$ Translating the LC$-3$ assembly language program into an LC$-3$ machine language program would involve converting the assembly language mnemonics into their corresponding binary representations based on the LC$-3$ ISA. This process requires referring to the LC$-3$ instruction set architecture documentation for the specific encoding details.